2 to the x = 9, many don’t know where to start

How to solve an exponential equation - practice problem.
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[@marytredinnick3366]

As a teenager, if i I could have looked in the future and discover I'd be studying algebra/math as a senior (60 year old) for FUN I'd think I'd lost my mind😂❤❤❤

[@rustynails8756]

Same here, I let myself fall victim to the girls can't do the math myth of my day. I have since then discovered I just love doing problems to relax

[@alexcabrallive]

Me too at 45 😂

[@gemox3225]

I feel the same and I'm 62.

[@alissagonzales735]

I always like algebra, plus geometry, trigonometry. It was plain simple stuff in the early years I hated.

[@cherylannebarillartist7453]

For sure!!!!!!! It’s SO reassuring to recall/relearn it through this very patient teachers guidance! It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here!

[@tschantz]

The video starts at 11:15 for those wondering

[@EE-Spectrum]

Yes, I agree. He took too long to get to the point.

[@FA-uf7vr]

If I were in your class I would have fallen asleep half way through your explanation.😂

[@Epoch11]

Thank you

[@fazayoubi7425]

Thx bro

[@Peterseng24]

To solve this what needed is the definition of the logarithm, a calculator and 15 seconds. 🇦🇺

[@res00001]

Just reading some of the comments. I find it interesting how many seniors (like myself) enjoy doing this for fun. Great Mental Exercises. Thanks!

[@toddspires603]

I'm 58. Stumbled across this video. I love reading the comments

[@Fernando-qd4ur]

Can a 39ish apply for the club?

[@CasaErwin]

@@Fernando-qd4ur Such a child!! In 21 days, I will be 89 years old.

[@Fernando-qd4ur]

@@CasaErwin 🤣🤣🤣

[@shaktisharma9525]

I m 53 now, enjoying watching this

[@cherylannebarillartist7453]

Thank you for offering this here!!! I am part of the 60+ club here! ✨🎉😅 It’s SO reassuring to recall/relearn it through this very patient teachers guidance! It’s bothered me that I’ve not used it and therefore have lost it, so yes! It IS. both fun and cognitively reassuring to do it once again here! You are indeed doing a great service to many, kind sir! Again, thank you!

[@marytredinnick3366]

🥰 totally agree

[@rlewis1946]

I’m 77, going on 78 tomorrow and I’m here, too. Thank you for this math lesson, that brought back many memories! RL

[@brandtbecker1810]

LOL - 60 is just right around the corner for me. (Where did the time go??) I was not crazy about math in high school as it seemed like they always went too fast. I liked my math teachers, though, I just had trouble keeping up. In college, I began to like it a bit more as made more sense the second time around - and I only had math classes every other day. Now it has become an enjoyable of a hobby for me next to collecting classical music CD's. BTW, one of my former math teachers, dear old Mr. Robert Parks passed away one year ago this month (in January 2023) at the age of 93 - may he rest in eternal peace!!

[@alvingoodman6539]

My wife does word puzzles to try to stay sharp. She is 70. I am 72 and trying to stay sharp doing and re-learning math. My 11 yr old granddaughter helped me get started by asking me to help her with her 6th grade math. 😅

[@marytredinnick3366]

🥰❤

[@Hugebear222]

I actually enjoyed this lesson.I'm retired and just when I thought that I no longer had use for this stuff, I just found out how wrong I was.I think I just found something that I cam actually gravitate to.Keep the wheels in the old brain turning. Thank you so much. Keep up the good work.

[@chuckroe3980]

It's approximately 3.169925, so rounded to 3 decimal places would be 3.170

[@johnnyrosenberg9522]

Yes, he rounded it wrong. He just skipped decimals, no rounding what so ever.

[@theowenssailingdiary5239]

@@johnnyrosenberg9522 nobody cares dude

[@johnnyrosenberg9522]

​@@theowenssailingdiary5239That doesn't bother me at all, but thanks for caring.

[@EnriqueAThieleSolivan]

True.

[@michaelhunter2136]

It's usually best to get to the point.

[@dhtyler]

this guy never gets to the point

[@chrisjfox8715]

Depends on the foundational knowledge of the viewer. If this feels drawn out then it's not for you. Fast forward

[@falcalv9793]

He really pisses me off with all his stupid rambling

[@user-fo2qj5ez6n]

16 minutes to explain this problem is ridiculous

[@falcalv9793]

@@user-fo2qj5ez6n this is why I unsubscribed from his channel. Too much rambling and his childish "Mr KZbin Math Man" really gets on my nerves. I will find someone else more mature to listen to.

[@philspencelayh5464]

Must of done this 30-40 years ago and completely forgotten because I've never needed to use it. Quite satisfying that it came back when explained, I'll be watching more.

[@paulbaker3527]

Its 55 years since I first learned this material and now I have almost completely forgotten it. We had Log Books back then, calculations were slower and calculators were only just emerging. I never used manual algebra or calculus in my working life as computer programs took care of multiple data streams and operations almost instantly. Now, I'm relearning the fundamentals solely to keep my mind active. Thanks for your explanations and patience.

[@mariondavis5735]

78 calculators didn't exist in my school 14:46 years. We used llog books.

[@paulbaker3527]

Dad, an engineer, bought himself a Texas Instruments model and in 1974 he bought me a Colex. It was the first calculator in my year group but we still had to know how to use log books and slide rules well before and well after 1974! @@mariondavis5735

[@wwiiinplastic4712]

@@mariondavis5735 Most of the students I interact with would have a meltdown if handed a log book.

[@johnplong3644]

Same here It has be 45 years for myself I bet you used a. Slide rule

[@wwiiinplastic4712]

@@johnplong3644 I actually still own two. One is my grandfather's that he used during flight training in the Marines back in WWII.

[@DriverDad58]

Applying the concept of an inverse avoids almost all the little tricks and sayings that otherwise folks would need to remember. If you have multiplication, undo it with division. If you have a power, undo it with a root. If you have an exponential, undo it with a log. And if you have a log, undo it with an exponential. I've had amazing results with students when I explain it this way. Good luck all!

[@peterwagner3170]

This is like watching paint dry

[@cr-ei5jm]

if only they had such good videos when i was in 8th grade learning pre algebra! Math is one subject where videos really make a difference!!

[@MrBobbybrown7]

I appreciate your explanation! I solved the problem this way: log (base 2) of 9 for an answer of 3.169925. Of course my calculator allows me to pick any base and not all calculators allow that.

[@JohnMasseria]

That's what I did, didn't he round it incorrectly to 3.169? To three decimal places should be 3.170. Maybe this is already in the comments.

[@ChrisinOSMS]

As an engineering student it was seldom the calculus that gave me problems, it was the algebra that gave me fits because it was so far back in my education that I was out of practice. Practice and repetition keep the skills fresh.

[@garyr4211]

True. When I started my engineering education I signed up for Trigonometry and found out I forgot Algebra from high school even though I got A's. So I dropped out and took College Algebra. Long story short I finished all the math requirements with A's and graduated with B. S. in Mechanical Engineering PI TAU SIGMA the International Honor Society for Mechanical Engineers.

[@NoobeyTunes]

As an engineer, I worked it out *numerically* by trial and error starting at 2^Pi (just for fun), and adding decimal digits and got 2^3.1699250014425 = 9.

[@itanc1]

What the last lady said!!! I’m 53, retraining as an electrician and not impressed with my tutors grasp of maths so decided to revisit where i gave up at school - calculus! I found your channel and have had no sleep since! I love the way you present and the brisk but sensible pace. Thank you from the bottom of my pencil case!!

[@johnhadley7715]

This might bear out my contention that some STEM instructors are (a) not fully immersed/versed in their subject or (b) might have a little fear of the subject.

[@bong9476]

Maybe if he shortened his lecture then you could get some sleep duh!

[@RockyS1945]

I am 79 now and have had a professional carreer and graduated twice in college both in arts and in science. I had to take algebra three times to paas it. I am enjoying relearning algebra only now I am understanding it thanks to this exellent teaching. First time knowing how to use log functions. It's really fun!.

[@bonifaciobonifacia8679]

What? 3x, wd two courses, your teacher is terrible.

[@unkelruckuss]

Hmmm.... I took Calculus and Algebra 3/Trigonometry in high school. The handheld calculator wasn't invented or in mass production and we used a SLIDE RULE. I passed those classes in 1967 and have never used a slide rule since. However, it might be nice to see you math guys actually use one to depict the olden days on one of your videos. Thanks! 👍

[@jazz2012]

I didn't know until I was in my late 30's that I liked maths (sorry I'm English so we called it MATHS). I didn't know I loved maths until I found you at the grand old age of 66. I injured my brain when I had a fight with a car on a crossing a few years back and thought my intelligence had been knocked out never to wake up but it has so thank you. Give me a few maths problems, paper and pencil and I'm happy.

[@marytredinnick3366]

So sorry about your fight with the car. It's so nice to see I'm not alone with a love for maths! BTW...I didn't know the English called it maths. I always thought it was autocorrect throwing in an "s" My father told me our family heritage is cornish. 🥰

[@Ben-mk9ig]

I thought it odd that the English call it maths until I realized that no one says they are doing mathematic.

[@jazz2012]

@@Ben-mk9ig The American term is more logical. Look at gymnastics, the shortened term is gym not gyms. That said, I don't think we'll change any time soon.

[@CasaErwin]

I would use logarithms for this: 2^x = 9 log of both sides log(2^x) = log(9) x log(2) = log(9) x = log(9)/log(2) Of course you need log tables to get the solution. Maybe there's another way. But since 2^3 = 8 and 2^4 = 16, we know the answer will be somewhere between 3 and e4.

[@RisingwoodsGal]

Calculators

[@siewpeng6873]

Yes, I would use logarithms but with the help of calculator. Never got to learn how to use the log tables in school. Am born in the early 70s

[@rpruneau68]

WHile you're at it might want to bust out ye ole Abacas...

[@user-rg9bm2hm9v]

There isn't a solution to this problem, because there isn't a definite solution for it

[@user-rg9bm2hm9v]

Maybe this or that yada, yada.blah

[@lagautmd]

Use log-base 2 and it's even quicker. x = log2(9). Plug log2(9) into the calculator and you get 3.1699 directly.

[@markjett899]

My calculator keeps putting the parenthesis around the 2

[@CasaErwin]

@@markjett899 In this case it doesn't make any difference which base you use. Any base will give you the same answer.

[@markjett899]

@CasaErwin tell that to my calculator lol

[@carpingnyland8518]

In Excel, you can use either =log(9,2) or =ln(9)/ln(2) or =log(9)/log(2), or if you really want =2*log(3,2) or something like that.

[@williamwightman8409]

JOY and DANCING FEET! I rose to the challenge and recalled the solution method from high school math before I had to resort to watching the video. I'm 64, so it has been a while since I needed to do this kind of math. A small thing, but it made my day. A similar event happened when my high school son came up to me and asked how to solve a calculus problem 20 years ago.

[@fjp3305]

Great!! I went through Calculus III and Differential Equations many years ago and nobody explained to me like this what a log is. Thanks. I'm thinking of studying Math again to learn all that I forgot.

[@tijolinixpertin]

A lot of people on the comments complaining about the guy "delaying" and going through "unnecessary long explanations" before solving the main problem, but i might say that i totally disagree with that, i find it pretty difficult to take my brain to focus on memorizing or learning something when it is out of context, so i just LOVE SO MUCH this guy's videos, they always give lots of contextualization and that helps me out so much, i wonder if math at school would be more fun if my teachers stopped cutting through a lot of "unnecessary advanced things for your level" and started to focus more on theoric explanations before the whole computation thing, it would make things a lot more smooth specially in physics in my opinion 😼

[@billycm8370]

Am so grateful to be reviewing all this fun math and you are a fabulous teacher. Thank yoy

[@HalAtTheMoon]

I was always terrible at math in high school. Now that I’m taking college math, I’ve developed a sort of obsession with it. I love logs. They’re way more practical in real life than one might expect.

[@WombatMan64]

As the next number is also a 9 (3.169925) you should have rounded it to 3.170. But otherwise fine.

[@doncherf2610]

Yep, his teacher would have deducted at least a point and likely more for forgetting how to round properly. You wouldn't want to do this on the space program.

[@billyhancock7851]

I pressed 2& the Sq root button, then typed in 3.17 and came up with 9.000467877. Why do I need to type in the 0 on 3.17 (0)??

[@WombatMan64]

@@billyhancock7851 it's simply what level of accuracy you're talking about. 3.17 could mean anything from 3.165 to 3.1749999... 3.170 however limits that to 3.1695 to 3.17049999...

[@billyhancock7851]

@@WombatMan64 My bad! I thought that in math, 3.17 meant 3.17! Not +/- 3.17. Also it did come up with 9.000. I guess that I have a lot to learn. I should have paid more attention in school 🏫!

[@atimko4925]

All of a sudden I have a desire to learn the math I ignored 26 years ago. Just wanted to say thanks for posting. Sincerely, Your 42 year old student 🙂

[@lamper2]

I never got THIS advanced in math. It's like aerobics for the brain.

[@TheWeatherbuff]

Totally agree with you. I'm a meteorologist, and I have already forgotten most of the math we needed to learn to get through it. This channel is a good place to start... without the intimidation factor.

[@tradersendeavors]

This is easy lmao I learned in elementary

[@ericpemble4599]

Or BRAINLESS

[@thecasualengineer99]

I used to use a booklet for the logs (bit like aslide rule), sines and other functions. Calculators are just a handy thing to have

[@sachmostaub1990]

I love your site! Great explanations. I’m 72 and your channel brings back a lot of memories of high school math. Still remember this stuff.

[@fredogden936]

I'm 66. Now I remember why I hated math classes: long winded explanations that don't get to the point.

[@heco.]

same for me. it waste too much time.

[@johnhadley7715]

If these ‘teachers’ could envision themselves in a burning space and their life depended on getting this info out before the roof fell in, the ideas and process would get transferred much more quickly. Instead, we are stuck with the idea that this is a special kingdom, and the special handshake must be learned first….

[@kyleharris3]

AMEN!!!!

[@JohnDuzzi]

Math is the cornerstone of civilization. This guy is trying to teach you something.

[@johnhadley7715]

@@JohnDuzzi …and you could not be faulted for adding,”as painful as it might be.”

[@fallonclouatre7934]

Thank you for your calm demeanor and clear explainations. Do you have videos on statistics?

[@Jockstrap716]

Thanks! That was the best lesson I’ve had about math in my entire life it feel great to be able to finally understand how to properly figure out math in the order it should be done . I am in my 70’s and you could only imagine how it feels to be now smarter the my grandchildren😂😂😂😂

[@happybee0622]

I am a math lover and this class stands perfect to me! Thanks!

[@joukenienhuis6888]

Thank you for explaining it so clear. In the Netherlands I learned about exponential equations and logarithms at school long ago. Thank you for reminding me, only now I had to learn to use brackets on my phone calculator and type the log button first.

[@nicetasgrass1813]

Yay!!it’s so much easier to use with the calculator.thank you! I just subscribed you.your channel is a big help for me.I’m 54y/o studying algebra 😅!I have headache all the time !I found your channel very timely.❤been watching you for days now.thank you very much!

[@louise7552]

Ive been learning algebra and all wonderful mathematics from you i never learnt at school, im 60yrs. I realised i never understood the formula. Thanks to you i can do algebra in my head now just looking at your tests. THIS HOWEVER HAS ME STUMPED. I CANNOT UNDERSTAND YOUR EXPLANATION OF THE FORMULA. OFF TO TAKE A VALIUM, IM GOING CRAZY 🤪.

[@Anarodriguez-iw1li]

I’ve noticed that math keeps your mind sharp. At least by playing around with it since my grandson started school, I’ve noticed can find my keys easier when I put them on other than where they go. Reason being I can focus better even when I had an encounter with temporary dementia.

[@genecrosby3776]

This video should be titled, "How to turn a 16 second solution into a 16 minute video.*

[@Fitzrovialitter]

Yes, tedious waffle.

[@michaelgasiciel9317]

First thing that popped into my head wasn’t I’m excited to learn the answer but Kodachrome by Paul Simon.

[@marilynbables8071]

Instantly visible solution.

[@torstenbroeer1797]

Exactly what I thought. Well, to be honest I didn't need 16 sec. 😊

[@burkhardnamen1003]

😅

[@francoispotgieter7567]

I’m 45 now, and our Math Teacher way back then was every teen boy’s dream, she may have explained log quite perfectly, not sure, but its great to listen to your explanation while being able to focus!😂

[@carolmadore1405]

I’m a 78 yr. Old woman and only had 1 yr. of collage, but had Algebra 1 & 2 in H.S., but I really love math. This is familiar, I like it. 😊

[@TheChefmike66]

I dropped out of Engineering physics, and became a chef. I have always loved math, and this was fun. I remembered that it involved logarithms, but couldn't move past there. I watch a ton of math videos for entertainment, which apparently isn't a thing amongst my peers in the culinary industry... I am going to sub to your channel!

[@theresamclaird1572]

A really great teacher makes a huge difference.

[@QwDragon]

It's log₂ 9 by definition of log. And it can be rewrited as lg 9 / lg 2 or ln 9 / ln 2. I think the original form is more beautiful. Also I expected you to show how to get 3 decimal digits witout calc as you said in the begining of the video, but you didn't :(

[@myriamduke7775]

Hi I am a retired RN and I have always enjoyed math. Doing math for fun now.😊 Thanks for your channel.

[@robinclifton4182]

As an aeronautical engineer I struggled with maths all my life and now , thanks to your explanations, at the age of 88 years the penny is beginning to drop. Many thanks for your wonderful tuition.

[@AnalogDude_]

lol, hahaha Better late than never.

[@meatdog]

We always used our slide rules, pre small calculator days, to solve these types of problems . the slide rules were fun to use .

[@BrettCaton]

Isaac Asimov's stories had a lot of references to them, and it's funny how they disappeared so quickly despite being in his visions of the future.

[@Thomasnmi]

Slide rules and log tables. Brought back memories

[@Stan_55UK]

When clearing out our loft many years ago, I found my trusty Thornton slide rule. I explained to my then young son that it was what we used for a calculator back in the day. He ran to my daughter shouting "Dad's got a wooden calculator!" I always liked it, and the batteries never went flat...

[@CasaErwin]

Fynny thing... I still have a slide rule that I used many, many years ago. I was just looking at it the other day and found that I could no longer figure out how to use it.

[@davidslauson2412]

Yes, in fact that’s how I solved the problem in about 30 seconds. Using the log-log scales of an old K&E log-log duplex decitrig (4081-3) slide rule, I got 3.17 as the answer. One of the beauties of the old analog slide rule is that it simultaneously shows 2-to-the-x solutions for an entire range of numbers once the problem is set up (but with somewhat limited precision).

[@jerry2357]

Take logs of both sides, re-arrange and the answer is log 9/log 2. (Use whatever base you like for the logarithms, natural or base 10, as long as you use the same top and bottom.) EDIT: I think logs are much easier if you're over 60 and weren't allowed to use pocket calculators in exams (which were fairly new), but had to use log tables instead...

[@nickhill9445]

That's what I did and agreed, although I was one of the first years permitted to use calculators, and did use log books briefly in junior school. Think of a log as "What number do you need to raise the log base to, to get the number you are determining the log of. In this case, Log2(9) . If your tables or calculator doesn't have the log base you are looking for (in this case 2), then divide your log by the log of the base you are looking for.

[@jerry2357]

@@nickhill9445 You don't need to think about different bases for logarithms for this problem at all. All you need to know is log(x^y)=y*log(x), for logarithms of any base. So 2^x=9 gives log(2^x)=log(9) which gives x*log(2)=log(9) and dividing both sides by log(2) gives x=log(9)/log(2).

[@nickhill9445]

@@jerry2357 That is true, however, if you think about it as I did, then if you already have a log of the same base, the answer is immediately log(9). Take, for example, e^x=9. You could think ln(e^x)=ln(9) => x ln(e)=ln(9) factor out ln(e) => x=ln(9). Or if you understand logs from the base perspective, you jump straight to x=ln(9).

[@mhc3408]

Just what i thought , it takes 1 minute to explain. Not 15 mins 🥱

[@tomluongo6344]

⁠​⁠@@nickhill9445 the question is not e^x=9 but 2^x=9 so x=ln(9)/ln(2) and not x=ln(9) as you stated.

[@mariofilippi3539]

When I spotted your video I couldn't prevent myself from watching it through. I forgot about logarithms completely so thanks for that. Wish I had you as a teacher back in high school.

[@ottokriete1153]

I've always held that someone who has really mastered a discipline can explain an element of it in terms that ANYONE can understand. You are proof of my postulate , and I thank you for your service............. one of the many who are underpaid and under appreciated in our society.

[@colleenbraun5792]

No calculators when I was growing up. I had a slide rule and we calculated Logs manually as I recall.

[@divahc1]

We had a green and white book of all log values.

[@tywalraven4936]

A slide rule is a log table

[@jpptubie]

Of course, if you prefer or are more accustomed to using log to base e, you can also get the same result from ln(9) / ln(2)

[@ekhartgeorgi4412]

"log base 2 16 is equal to 4" is a very sloppy way of saying this that confuses people who need such a basic review. It should be at least "The log base 2 of 16 is equal to 4", better "The logarithm of 16 to the base 2 is equal to 4. (And it's not "log rhythm".)

[@CasaErwin]

You will get the same result regardless of the base.

[@RC-yb5dp]

This is bringing back fond memories for me. If I am helping someone, I always tell them that algebra is a lot of remembering.

[@user-ve1ss6is3n]

You break down something that seems so complicated and impossible to figure out into step by step instructions that are understandable I never understood this stuff in school now I know why no one ever explained it like this I'm 63 and I'm getting this ha

[@johnycash8291]

All senior citizens who hated math is here. 😂😂

[@joelwalk3728]

Maybe as a followup an explanation of Taylor and Maclaurin series (expansion) to illustrate the algorithm used by calculators for LOG SIN COS etc (the transcendentals).

[@zwebsterz]

OMG, the part of my memory hasn’t been touched for decades.

[@alberthartl8885]

Have not had to do anything like this since 1980. Brought back slide rule memories from the '60s.

[@aussietaipan8700]

This one is really cool; I did this in my head knowing 2 to the power of 3 = 8 so I knew the exponential had to be 3.something. So I used 2 ex X = 1 where ex = ,13 so the remainder for 3 is .17 therefore my answer is 3.17, slightly over but close enough in my head

[@mohasat01]

No, yours is exact! To 3 decimal places, it is 3.170 but to 4 decimal places, it is 3.1699. x = ln9/ln2.

[@jeremyfoster6942]

How can doing anything to a 2 with a 3 make 8??

[@simone7582]

I teach Maths. It’s better to over explain to help lesser able students. There are a lot of concepts needed to understand in order to solve this question. The final solution could even of gone further talking log laws. So I think the explanation could of even gone longer. I think your an excellent teacher. Taking the necessary concepts and explaining each part. So well done on your excellent channel.

[@kevinspradlin6288]

Thanks for a fun review of something I did decades ago...always good to keep the mind sharp.

[@velikijoxotnik]

Either log base 10 or natural log (ln) can be used to solve this problem. Take the log (or ln) of both sides, then use the log (or ln) property to pull the the exponent to be multiplied by the log (2) or ln(2). xln(2) = ln(9). x = ln(9)/ln(2) = log(9)/log(2) = 3.17. The base of the log doesn't matter.

[@davedixon2068]

my only question here is not how but why?

[@madhusudangupta3661]

​@@davedixon2068, Anyone who has studied math, knows x log2= log9. Those who do not have, can not understand this concept unless they take math class afresh. So the title of the vdo tends to ridicule those "some". The post could not teach math, enough to explain the concept of Log to answer your " Why" in the VDO.

[@madhusudangupta3661]

@ Chuck Pierce , In fact ' log x to the base a =b' means x raised to the power of a =b. X can be any number, be 10, 2 or e. The logic of Log does not differ. By the way, your profile and interest is impressive. ❤ from Bharat ie India.

[@davedixon2068]

@@madhusudangupta3661 You dont get it ,I am not asking why log whatever does whatever I am asking why work out any of these math problems using techniques that you will never use ever in your life

[@davedixon2068]

Thats why bother wasting your time

[@sistahsunshine]

This video is precisely why i still cant do basic math. Too much additional information in between the actual lesson. Please just tell how to solve the problem and keep out the million if whens. You must have said how do we solve this? Im going to tell you right now. JUST TELL ME. sorry. im not alone in this. Just ask anyone who failed math.

[@CarlosRio25]

Don't watch the video go somewhere else

[@AyoTunde-li8po]

He talks to much

[@BasementEngineer]

sis: You are not wrong. Many of the math teachers I had in HS and Uni. were terrible; however the two or three good ones kept the fire alive. I believe the explanation used by the author is TERRIBLE! Having taught technical college for a number of years I determined that the direct solution to the given problem is the way to go, followed by supporting theory. Deeper analysis may be justified depending on the questions from the class/group. Getting bogged down in the minutiae of the theory will put half the class to sleep before the actual solution is proffed. BTY, I "solved" this problem by estimating the answer to lie between 3.1 and 3.3. Good enough for a first go-around.

[@adrianm.2043]

I don't know what drew me to your blog, but it is really interesting to find how much I have forgotten since I was at school and later did my degree, I am seventy now and don't really have much use for maths, except I have a couple of grand children one two and one seven, I am helping the seven year old to learn to read, maths could be next. So I decided to subscribe to your channel and relearn or refresh or even learn new things in Math. Might help prevent the mind addling as well. I love the way you explain things so clearly, you must be a talented teacher.

[@jack002tuber]

Fun fact, the answer is LOG 9/LOG 2 no matter the base. Try LN 9/LN 2. Works. There is a law of logs on how to get the log of any base. Look it up. You'll thank me

[@starman5754]

Great video. Learned this stuff in Alg 2 at age 16 and honestly have never had to solve for an exponent in 50 years since, even though I've been involved in highly technical areas the whole time. I HAVE however used straight Log, geometry and trigonometry functions a LOT. Electrical/audio, frequency/filters/phase, db all live deeply in these math zones.

[@misterlau5246]

Same here 🤝

[@CasaErwin]

straight Log???? Not familiar with that term. Is it anything like natural Log?

[@starman5754]

@@CasaErwin Log 10 is most commonly used and referred to just as "Log" and was my meaning. I learned about natural log as well but never had to use it in real life.

[@CasaErwin]

In this particular problem, as is the case in most problems involving logarithms, the base is not important. You will get the same result no matter what base is used.

[@TheWeatherbuff]

I wish I'd had teachers that took time to explain all this stuff like you do. Most of mine just expected us to know it by "reading the books". That's tough for visual learners. May I ask which program you are using for the illustrations? I'll be joining your Patreon crew. This stuff is gold! -Steve

[@maya_coqsalonga]

Looks like MS Paint on a surface laptop.

[@goodkawz]

5:30

[@Max47340]

Excellent video on the basics of logs and exponents! Thank you, sir!

[@brightmoon7132]

When I was in school I never understood algebra, despite some very good teachers. I felt bad about this for a while. Then once I got out into the real world and discovered I NEVER encountered a single situation where I needed algebra. The icing on the cake came years later when I had a neighbor that was studying engineering and was a real math whiz- AND HE TOLD ME ANY MATH PROBLEM THAT CAN BE SOLVED WITH ALGEBRA CAN BE SOLVED WITH ORDINARY MATH. The only difference is the way the problem is stated. For example, the above problem is really a fractions (or decimals if you prefer) problem. Math is natural, even some of the higher mammals understand the basics of it. Algebra twists it into something contrived, artificial, and over complicated.

[@incub8]

I didn't have an advanced calculator handy, so I used similar logic that the value of X should fall between 3 and 4. From there, I did it by inspection. My first guess was 3.333 and that was a bit over 10, so then I tried 3.2 and that was 9.18 ... after that, it didn't take too long to get it. 😄

[@marlenesunley381]

3:38 3:38 4:28 oo😊oo😊 ?;-. add e❤

[@CasaErwin]

In my opinion, guessing has no place in mathematics.

[@incub8]

@@CasaErwin - Like I said, I did it "by inspection." This is a valid technique in mathematics when a person does not have a calculator. There has to be a starting point, which involves an initial "guess," albeit, it would be an educated guess, based on experience, etc. By your logic, you would never approve of the Scientific Method which is to take a situation worthy of investigating and stop there, rather than creating a hypothesis,, which in essence is also an educated guess. We would have no technological advances if people didn't start processes with guesses (hunches). Jeepers.

[@victoriabreitbach6924]

I am iin my 60's and have always enjoyed math. This can be very confusing! I wish you would let us know when we would use this in every day life. So that I can explain it to my grandchildren that struggle with math.

[@brucestaples4510]

Everyday life just does not call for this. Addition, subtraction, division and multiplication should get you through life. Olives: 3 for $5.00. How much is one? THAT'S what ya need. Unit pricing basically. If you can't remember the last time you used exponents, THERE'S the reason - ya don't need them...IMHO. 😁

[@victoriabreitbach6924]

@@brucestaples4510 Thank you for your response! I have learned so much from your youtube site. I have 5 children and some thrive on math and others struggle. Many will ask what they need it for and you have answered as I have told them. There father was an accountant and loved math I believe that they found this as something that they enjoyed together. Again thank you for your quick response. Take care Vickie

[@davedixon2068]

@@brucestaples4510 Totally agree, better by far to get your grand kids totally conversant with mental arithmetic being able to add, subtract, multiply, divide, and average in their heads, without a calculator, will be far more beneficial to them, they need this to pass their exams they need mental arithmetic to live comfortably for the rest of their lives. Basics first!!

[@sammic974]

you might use it for calculating compound interest on a loan.

[@davedixon2068]

@@sammic974 thats what financial advisers are for

[@891Henry]

When I was in school in the 60's and early 70's we had no calculators and used log tables. I remember how much I hated logs. Exponents were ok but not logs. Thanks for the info. I am another senior who is hooked.

[@richardcommins4926]

Note to math instructor: Anytime you use a log identity like Log a^c = c*Log a, you should stop and prove that to your class again. It would take about 1 minute each time but it would reinforce the log identities to your class to help them memorize them and if forgotten, how to prove the identity and show why they are true. Yes, when we get to the advanced algebra classes, this should no longer be necessary anymore but for an algebra 1 class it would help to reinforce the identities. Another way is to make a one page sheet with all the proofs and each time they are used then refer to the proof sheet. This will drill home the Log relationships and why they are so. We all try and memorize these tricks but sometimes with time, we forget. If you know how to prove the identities, then they will never be lost to a bad memory. The only thing that really has to be memorized is that Log of a to the base x or Logx(a) = b is the same as a = x^b and everything else is derived from that.

[@anthonypanneton923]

if you don't have a calculator, just use your slide rule. :)

[@lorettanericcio-bohlman567]

Abacus?

[@davidsalvia6294]

Often in physics, engineering, and chemistry, 3 significant digits is wanted, and when the fourth figure is 5 or greater would round up, so 3.169925 would round to 3.17.

[@invaderzim1964]

With significant digits, you must follow the rules not just arbitrarily round to 3 digits. The significant digits depend on the precision of the measurements.

[@scottcoston7832]

⁠@@invaderzim1964good point… If someone knows the context, and the basic mechanics, they are likely aware of significant digits. Your post was useful for those who are unaware. In a nutshell, more numbers to the right of the decimal sign reflect greater accuracy. In this case, 3 digits might be appropriate depending on the context. It is not appropriate to use precise decimal numbers since their use implies accuracy. Someone asserting tomorrow’s high temperature will be 83.2 degrees should have used an integer

[@jimgunning670]

I am ' old school ' 😢 65, but when it comes to teaching, I have never come across a teacher like John. He makes the most difficult problems look easy😊. Who is this guy? ? John, the problem is solved using base 10 and e. Why ?

[@jimgunning670]

John. Am I to old to study PDES ?

[@randomonlineactivity]

Last math class I took was AP Calculus AB 16 years ago. Somehow, I could still figure out the answer. You took a long time explaining it.

[@ianbelletti6241]

Now you need to show us how to complete this on a slide rule.

[@js5665]

Whoa! Now you're talking Advance Cave Man from the 1950's to at least the 1980's who had access to the magic stick called A Slide Rule. I'm a cave man from the 1960's with just a pencil with an eraser and stacks and stacks of paper.

[@anastasiae.5338]

I think what our procedure 900 years ago was to isolate the x. By multiplying both sides by the base. Which turns out to be the same thing, but I think that's how they put it to us back when I was much younger.

[@robertwendell1556]

Very simple! All you need to know is what exponential and logarithmic functions are and what their relationship to each other is. They undo each other. In other words, they're inverse functions, like addition/subtraction, multiplication/division, etc. By definition, raising a logarithmic expression to a power is the same as multiplying by the exponent the logarithmic expression without the exponent. 2^x=9 ln(2^x)=ln9 x*ln2=ln9 x=ln9/ln2 x=2.19722/0.694315 x=3.1699 2^3.1699=9 .

[@MichaelFenley]

Love the examples you provide to parallel the problem. TY

[@tarkasify]

You don't need 16 min to introduce log or natural log. Respecting time is crucial for a mathmatician.

[@ube-23s]

Finally, somebody said something correct. I wish he had not spent all that time explaining the actual problem. Edited message. I forgot """not"".

[@stanleybaehman7214]

His loves to hear himself talk and tell you how smart he is; which is the exact reason so many students are turned off by math!😮

[@ube-23s]

@stanleybaehman7214 Or I don't know if youtube pays them by the time .

[@anthonylosego]

It's the algorithm. They need about 12 minutes.@@ube-23s

[@visaman]

​@@ube-23svideos have to be 10 minutes to get advertising revenue.

[@longshankdrills8799]

Holy crap dude, spit it out, get on with it !!! Almost 5 minutes in and you've done everything but explain how to solve the problem.

[@ClayChef]

I totally agree. I would’ve also appreciated how to solve it WITHOUT a calculator. Log 9 divided by log 2 equals 3.169? How do you manually come to that conclusion? What’s the value of log? Is it 10 or 7, and how does that apply? I ended up with more questions than answers here.

[@tonyrhodes5541]

Yeah I had to turn him off. I feel for the kids in his class. Did you see the video he did about pemdas? Terrible

[@davidslauson2412]

This is an example of a kind of problem that was easily solved on the old (pre-calculator) log-log slide rules. I pulled out an old slide rule and solved it in less than 30 seconds, getting 3.17 as the answer. One of the beauties of the old analog slide rules is that once a problem like this was set up, it simultaneously provided an entire range of solutions for 2^x=y problems, within some limits of precision. Slide rules are completely built around logarithmic scales and embody logarithmic manipulations (almost transparently) in everything they do.

[@MarilynBurgeson]

Yes, it makes more sense using a slide rule with a log scale.

[@makerofstuff]

At 70, girls didn’t need to learn this. It would have been a waste of space. I am delighted to find your channel!

[@mtlmike3956]

Way too many filler comments and long explanations. I zoned out many times with the monotone delivery.

[@random_precision_software]

You need to half the video lengthy, cos it goes on way too long.. It gets boring!

[@jeynjohnston8085]

Thanks for the refreshers!

[@eagle32349]

for 2^x = 9, the solution is x = log2(9). When you substitute you get 2^log2(9), the 2 and the log2 cancel out and you are left with 9 as a regular number, then it's just 9 = 9.

[@redapahlawi-ki9of]

TOO MUCH UNNESSESSARY EXPLANATIONS FOR SIMPLE QUESTIONS ...

[@coureenlawrence4915]

I agree..

[@ModernGolfer]

WHO the heck, over 60, comes on KZbin and watches math videos just for fun? Oh, that's right, *I* do! 😁 Fun, AND to learn something I didn't know before. 😉

[@destinyreturns4885]

I got a "D" in high school geometry, and that was from my high school football coach (I was pissed), but in college I had a TA that somehow turned the light on for me in Algebra and I ended up becoming an "A" student in calculus. After 40 years on the "working" world I seem to have forgotten all I learned. so I'm having fun with these lessons, but truth be told I never used any of this to earn a very good living before retiring.

[@venkatesank3841]

Well. Solution is very simple. 2 power x = 9 X log 2 = log 9 X = log 9 ÷ log 2 X = 0..9542 ÷ 0.3010 X = 3.17 is the answer

[@conatencion-kd3io]

Thanks for your videos. I do appreciate your time in explaining your rationale to each step.

[@funprog]

Always take the log of the base which in this case is 2. Simple : log2(2^x) = log2(9) => X=log2(9)=> x = log2(3*3)=> x = log2(3) + log2(3)=> x= 2log2(3)

[@paulanizan6159]

In my day, we still had grade 13. I really enjoyed Math in that grade, especially calculus.

[@malcolmdonaldson3297]

Thanks for this even though I made it through calculus, I really had no concept of logarithms. This went a long way to opening up my understanding .

[@hotflashfoto]

I've never understood logs, but with this video they now are starting to make sense.

[@mitchilito99]

Love love love your teaching style.