11 - (6 to the x power) = 3, x =? “Let’s solve this exponential equation one step at a time!”

[@thomasmaughan4798]

I appreciate the refresher. I went through high school with a slide rule which uses logarithms natively. It's how it works.

[@drziggyabdelmalak1439]

Thanks for explaining the 'log' situation so clearly.

[@pontiacwssix]

Liking the tutorials.. Can you create a chart of common rules (exp, pwr, quotient) etc and place them in a vid so they are all together. Also it good to explain why you got rid of the negative (divide by -1) becasue you can't have a neg log input.

[@devonwilson5776]

Greetings. Certainly, we can solve it. This is how we do it. First we restate the expression 11-6^X = 3 as -6^X =3-11 to get -6^X = -8. This is the same as 6^X =8 after dividing both sides by minus. Now we will say Log 6^X = Log 8, and X Log 6 = Log 8, now we will isolate the X by dividing each side by Log 6 to get X = Log 8/ Log 6 = .90309/.77815=1.16056, rounded to 1.16. We have done it and we have done it correctly. We know that our answer is correct because 6^1.16 works out to 7.9920, approximately 8, and 8 taken from 11 gives us 3.

[@jesi3336]

Was always better at the visual geometry than formula algebra. Always wanted to strip formulas down as quickly as possible. For me...I just automatically assessed that if I needed to get to an answer of 3 subtracting from 11...it had to be 8...but 8/6=1.3333........ I do not recall my math classes from (yrs.ago) including "logs"....my memory fails or inadequate instruction😮

[@SlideRSB]

I prefer to go from 6^x=8 to _log base 6 of 8_ as the exact value and then use the property of _log base b of n = log n / log b_ to get my decimal approximation.

[@paulpurpura191]

Make sure that you know how your calculator handles PEMDAS. When I went to check my work, when I entered “11-6^1.16”, I got an incorrect t result. I had to enter “11-(6^1.16)” to get the correct result. I HATE the new PEMDAS!

[@denisrenaldo3506]

In France and in many other places, we use Log for a neperian logarithms and log for decimal ones.

[@daniellereid6539]

I don't know how I passed high school math! As soon as you started using math terminology I was lost.

[@genelowry5666]

6^x=8 => x=log 8/(log 6) => x=approx. 1.1606

[@drziggyabdelmalak1439]

I'm in the middle of doing a BSc Maths degree here in the UK as a retired person, so you can work out that I studied Maths at school quite a while ago!...and it's interesting how so many [what seems to me, at least] basic, simple ways that we did calculations now seem to be more complicated [to me at least] yet are presented to the kids [here in the UK] as simpler!!! So in the intial equation all I'd do is say: take 3 and -6^x to the other side and swap their signs! And you get 8 = 6^x!!! Yet, we now have to subtract -11 from both sides, then divide both sides by -1! Boy...what a hoo-ha!

[@thewolfdoctor761]

I agree. I'm a retired American and it seems like today's math requires numerous unnecessary steps.

[@zitherzon2121]

You must remember that here in the USA more than 50% of "urban" public high school students cannot do even basic arithmetic (and many cannot read and write.) These are probably the students he is speaking to here.

[@thewolfdoctor761]

@@zitherzon2121 I read that 40% of Americans can't find Canada on a map. How are they expected to know basic mathematics?

[@zitherzon2121]

@@thewolfdoctor761 Of course you did notice the "public school" and "urban" qualifiers in my comment? And in the USA, "arithmetic" is not considered by most to be even "basic mathematics" or Maths? Is that the proper slang in Canada? P.S. Sending some buses north to your border (trains next) so you too can enjoy proper diversity.

[@Sharonjrainey]

Thanks you’re terrific

[@loiza59]

I wonder if you can solve the problem using the square root of 8/6? x= square root of (8/6)

[@Viridian88]

I'm not sure if I solved it correctly. I made it until 6^x = 8, then I merely applied the very definition of logarithm itself, that is: a^x = y x= log(base a) of y. That leads me to x= log(base 6) of 8, but since 8 is 2^3, you can rewrite it and move the exponent before the log term. The final result is x = 3*log (base 6) of 2, which should be exactly the same number, 1.1605...

[@jeffreyhearn8930]

Why confuse things when the calculator stores in log base 10 o log base e?

[@Viridian88]

@@jeffreyhearn8930 It's still the same number, there's the change of base formula anyway.

[@blackmonstermonster5484]

Log with base 6, 8 (or) Log~⁶ 8

[@cobbler88]

Cool. I was more interested in being able to properly set up the equation to get the final answer rather than actually solving for it, so I'm happy with how I did.

[@juliestevens6931]

I have never done a problem like this, so it was fun to learn. I also learned that on my iPhone calculator, I have to click # Log/# log = to get X If I do log #/log # it is wrong - close but wrong. Cool!

[@cobbler88]

I don't know that I can recall doing problems like this, although i went through trig and pre-calc so I likely did. I just wanted to be sure I could set it up properly without actually doing the homework to produce the actual answer. I'm satisfied with how I did.

[@BlackhawkPilot]

Goes so much more quickly when you have some memorization of logs. In Swiss school we had to memorize the logs of 0 - 10 and it is amazing what you can do with just those 11 logs.

[@h30202]

Wow!

[@arishsheikh3000]

What us log0

[@thomasmaughan4798]

@@arishsheikh3000"What us log0" If I remember right, it's just 1. No, that's the log of 10. Log10=1. 10^1=10. 10^0 might also be 1, by rule.

[@SlideRSB]

The logarithm of zero is undefined.

[@HeatherRose2023]

How were these equations solved before calculators? Good to know in case the batteries die.

[@pinpointmediadesign]

Before calculators, you used logarithmic tables. You simply looked up the value in the table.

[@michaelb866]

Thank god for this tutorial. I use this information every day!

[@cobbler88]

Right? We're not all in the logging business, for God's sake!

[@bradparker6156]

It gets a whole lot more interesting if the unknown (x) is in exponent and at primary level. (Like "11x-6^x=3", perhaps no solution?)

[@TLouise1959]

If I had a teacher like you I would have been a little math wiz. Instead I was made to feel stupid

[@cobbler88]

For all of you people who - when commenting on basic algebra vids - claim that you never use it in your daily lives, THIS is the math you're actually thinking about.

[@louf7178]

9:00 Could have mentioned this could be written as log base 6 of 8 (but would not be able to use the calculator logarthim function).

[@striker8380]

Modern calculators allow you to input the base you want to use. So x=log(base6)8 = 1.16 no need for all of the extra steps

[@rasheawhite3644]

Not my field of expertise. But I guess I am willing to learn. Took it middle school and high school. Algebra and geometry are those courses I really have to focus on. I failed algebra my freshman year of high school. Well, I did not have the best teacher that could teach it. Took algebra my Sophmore year of high school and passed with an A. I had a GREAT algebra teacher!😊 The next year while sitting in geometry class I received word that my teachers from my sophmore year got together and voted me into the national honor society. I was surprised!👀 What a difference a year makes when you stop chasing the approval of peers and focus on what you love... learning and being a great student. Math is the subject that I can and gave passed with descent grades, but math is not a passion of mine. I will stay in my lane and leave math up to the experts and those who excel at it.😂🤣 Know your lane.

[@eliasalonsagayfernandez2890]

Please simplify the operation

[@ronrestaino8182]

Don't listen to the complainers. I watch all 369 videos and I enjoyed them,

[@onion6foot]

Could you explain logs without calculator?

[@TheloniousCube]

It's the inverse of raising something to a power 3 to the power of 2 is 9. We can ask "To what power would we need to raise 3 in order to get 9?" The same question can be asked as "What is the log base 3 of 9?" Because of the way powers and roots work, it's possible to shift the base so as to work with a common base (usually either 10 or e)

[@momdebomb]

I get 1.33 and it seems to check out - what am I missing? 11- 6^x = 3 isn't this also - 6^x + 3 = 11 and also - 11 - 3 = 6^x ? going with the last one - 8 = 6^x meanwhile back at the brain twisting bit ok so 6^1 = 6 too low...and 6^2 = 36 not it It's not a whole number but it does start at 1 x = 1._____ Let's subtract 6 from all sides because we know there's a 1 now which is one 6. 1._____ becomes ._______ and 8 - 6 = 2 I don't know the correct notation here but I hope you get my drift That decimal bit has to fit into 2 six times. 2 / 6 we get .333 forever add the 6 back for x x ≈ 1.333 It works out when I check 1.333 x 6 = 7.998 11 - 7.998 = 3.002 Love love love your channel

[@thiennhanvo2591]

How did i get x=1.1 in the first glance..?

[@charlessands6933]

I understand how you got the answer of 1.16 but it seems like the answer should be 1.33 and here's how I got that. Just looking at the equation is 11 - something is 3 well obviously 11 - 8 is 3 so we know that six square has to be eight. I'm 6 * 1.33 is very close to 8 (7.98). When you multiply When you subtract 7.98 from 11 you get 3.02. How can what I am saying seem to be correct but apparently not be correct.

[@juliecranford534]

I know you’ve moved on from this, but you’re multiplying 6 X 1.33 and getting 7.98, but the problem is 6 to the power of X. I know you knew that, but somehow were pushing wrong buttons on your calculator. Or phone-which is probably the problem.🥴 I was struggling with that. Hope this helps-if you even care a week later.🤣

[@charlessands6933]

@@juliecranford534 : I don't know why I didn't realize my error earlier. I just smacked myself. Thank You.

[@juliecranford534]

@@charlessands6933 No problem!! I know how frustrating it is when you get stuck on something like that. I knew you totally understood but were just making a simple error. Have a great day!

[@theanalyst9043]

@charlessands6933 -- I'm going to agree with you no matter what spin the math gurus put on it.

[@TheloniousCube]

It's not 6x it's 6^x (six to the power of x)

[@aryusure1943]

Well, I got to minus 6 to the x = minus 8. After that, I watched the video. ;) Getting there but I need to do a better job at identifying the different types of equations for sure.

[@frankp3748]

I solved by elimination..started with x= 2, then slowly reduce it till i get 1.1606

[@jeffreyhearn8930]

This process takes too long.... can be done in 10 seconds on a calculator...

[@Torby4096]

I had a prof mark one wrong when I answered 7 sin(30). She wanted a number, but my calculator was not in my backpack where it belonged.

[@user-ky5dy5hl4d]

At 11 seconds in the video. John. It is not eleven minus six x equals three. It is eleven minus six to the power of x equals three.

[@michellepopkov940]

As they say in The Holy Grail “Get on with it!”

[@dwaipayandattaroy9801]

😊11-(6)^(29/25) = 3 😊

[@h30202]

😱 How did I pass my college algebra, Pre-calculus? 🤔😂

[@user-zx5xw4yw2e]

I'm super confused 😕 😂😂 Guess I need to go back one level. Lol. (I'm a Reading, Writing, and English gal.)

[@louise7552]

I hear you. No idea. Was English and History girl 😮.

[@shleeabcd]

ask the chatgpt and return the result is approx. 1.34985...

[@Nikioko]

8:40: This is not the final answer. The final answer is x = log₆8.

[@Weidl01]

I had the correct solution right away but watched the whole video to see how you would solved logs without a calculator... Turns out i misunderstood the assignment here and we simply have to use the calculator😢

[@user-ri6rn7ti5h]

11-6^(2)=( 36 -11)= (25 ÷7)= 3/4

[@vineyanand-ed7hg]

Calculation with log is very easy. Can you solve it without log? Challenge

[@singhanand3333]

1.1605

[@petesmith9472]

I got as far as saying 14=6x… 😊

[@chanyinwong9845]

Using log..？8=6^x

[@pingechelon9389]

Log 5 / Log 6

[@leetrask6042]

Approximately 1.1

[@danieldennis9831]

6^x=8 log6. Okay I have to watch the video first to figure it out.

[@user-ky5dy5hl4d]

Can't you cancel logs and be left with x=6/8 ?

[@user-ri6rn7ti5h]

(Log6/LOG11÷8)= 6.13

[@fleurettewilliams6077]

I am doing ged math and really need help on fractions and other decimals is ok algebraic knows nothing

[@lindakennard8770]

Where' the 'bacon and egg" formula?

[@lugnerthelisma1246]

8/6

[@user-ri6rn7ti5h]

Log6/LOG11= 3/1

[@jobisrael8313]

I give up on this one I don't know the steps for this😂. 08-26-23

[@johncrosby5570]

It took you over 10 minutes to show how to evaluate a simple equation that can be described in a minute. You digress to excess!

[@koomsonbright9017]

Answer is 1.1605

[@glennherron9499]

I do most math problems like this in my head, don't need to write the steps down.

[@user-lg5zm9yw4f]

Yes. I can solve that problem

[@DaveRossignol]

Love this channel. Constructive criticism might be that you tend to be a bit too klong winded. You give 100% for 1.16 answer. Hmmn. Note that the answer is an approximate answer, so you shouldn’t be giving 100% for this answer. Seems to be a bit north of the North Pole. Appreciate your channel. Thank you

[@user-lc1ss5we6z]

15

[@msms3260]

Great nuggets of knowledge, but would be more easy to listen if not so long winded and unnecessary repetition of same thoughts. Economizing words will be good.

[@oldschoollew]

x log 6 = log 8 x = log 8/ log 6

[@forrestgreen9369]

x = log 8/log 6 = 1.160558...

[@jesseslack2089]

This was fun...but even as a kid in the 80s there was no real need to learn math cause of technology..

[@rajariaz5928]

7

[@arekkrolak6320]

How come you take 10 minutes to say log6(8)? Also the result is irrational, you cannot express it as decimal

[@baconp1318]

X = 8/6.893233 and so on

[@jeffreyhearn8930]

log8 ÷ log6...... an extremely basic exponential equation

[@zitherzon2121]

Tell your students about the GIANT insurance companies who their pay mathematics actuaries very well still in 2023 AD.. (Hidden Figures for sure.)

[@user-md6cv9rc9t]

I got x as 1.333 6x1.333=8 or7.998

[@theanalyst9043]

By some formulaic contortion, 1.16 x 6 = 8. Funny/fuzzy math. I'm not playing.

[@TheloniousCube]

It's not 6x it's 6^x (six to the power of x)

[@TheloniousCube]

It's not 6x it's 6^x (six to the power of x)

[@momdebomb]

That was TheloniousCube^2

[@nickrich56]

the answer is 5 ..,😁

[@edstraker8451]

Easy. 47000000567.4. I love maths.

[@evertvanderhik5774]

Quite basic stuff this

[@Teams-ex7rd]

Trident 🔱 devils -

[@Nikioko]

6:05: That is wrong. log is the logarithm to any base. If you mean the common logarithm, you have to write either log₁₀ or lg.

[@nicklaus8536]

The problem is he talks too much, which turns a very simple equation into a very long story. Students will be bored

[@LB__1]

I see that I am not the only one feels that way. That whole time I was saying, "Just get to the point."

[@irishva2314]

When you carry it it's actually 8=1.33 (7.98).As close as you can get to 8!

[@atraxotoxin3840]

That's what I got it's actually 1.335. If you prove it out the way he is explaining is wrong. It comes out as 4.04. If your tring to find x to make it equal to 3 then the number is 1.335 for x. 11 - 6 × 1.335 = 2.99. That's about the closes your going to get to it equaling 3.

[@TheloniousCube]

It's not 6x it's 6^x (six to the power of x)

[@TheloniousCube]

@@atraxotoxin3840 It's not 6x it's 6^x (six to the power of x)

[@atraxotoxin3840]

@@TheloniousCube ok thanks

[@kathyrivera1179]

third

[@gemgal711]

Simplify simplify simplify ffs

[@gbaderojamesjoshua]

The answer is 8

[@srdjannalis3037]

Too simple.

[@audreydaleski1067]

Nat log... let's do some real math.

[@damionsoul5318]

You say too much

[@mikehood6745]

Simply cannot take seriously a "tutor" who keeps reading out 6^x as "six x".

[@mikehood6745]

Watched a bit further and heard, "I can simply divide -1 by both sides of the equation." Just sloppy. So glad I don't have to try and learn maths from this guy. Don't have the fortitude to watch the rest of the video!

[@homeauburnRaja-hm3gq]

X=3/log3

[@Fausto12345.]

Who really cares. As a former music educator I always wondered how this makes anyone have a better life. You will never have to solve an equation or dissect a frog but being part of a music program will make your quality of life better.

[@sue2611]

Wow! That's an interesting attitude for an educator. I happen to enjoy math, and it very much enhances my life.

[@skillet7805]

When where why how for what would there ever realistically be a decimal in an exponent 6²=6*6 6¹.¹⁶ solve that And I'll accept it Students if this can't be solved like this if letters have to be used to solve this Quit this class It's a waste that is not a joke

[@thomasmaughan4798]

Fractional powers must be solved with logarithms. It cannot (probably) be done algebraically. Deep in the guts of your calculator that's exactly how it handles exponentiation problems. Decimals in exponent is how a slide rule works! two times three, on a slide rule, is actually the antilogarithm of adding the log of 2 and the log of 3. Adding Logarithms IS multiplying! Log2 + Log3 = Log6. The mechanical property of a slide rule can ONLY ADD. That's what it can do. 2 inches plus 3 inches is 5 inches BUT when using a log scale, it's 6! So, if ADDING logs is really multiplying, what happens if you multiply Logs? Well, that's exponentiation. \ Log2 = 0.3010 (and some digits Log3=0.4771 Sum = 0.778 antilog(0.778) is 10 to the 0.778 power or 10^0.778 = 6 Log3=0.4771 Log30=1.4771 Log300=2.4771 Notice an interesting pattern. The whole number is the power of ten, in simple terms, how many zeroes! This is why a slide rule can calculate 2*3, or 20*30 and get "6" but you have to mentally put the decimal place where it needs to go.1 + 1 = 2, so the characteristic is 2 and that means the answer is at least 100 but less than 1000. That makes 600. you know the 6, you know it has 2 places (times 100) so 600.

[@mrfrosty42]

a lot of rambling - and typical of maths teachers in school - how to switch you off in 10 secs

[@janetfilger8326]

Who cares? I hate math.

[@jackiecote203]

LOL. This comment made me laugh so much. TY for that. Algebra always confused the hell out of me and it pissed me off. Just couldn't make it click so I decided I hated it. Thanks again for the laugh.

[@belkacemtalhadjt3868]

You speak too much.

[@timhannah4]

Stop the funny faces and PLEASE just show the resultant with ALL the RUBBISH!

[@johndemeen5575]

It’s not important. Boring.

[@louf7178]

You won't be saying it's not important when the cabbage is coming out of your wallet.

[@ioannisimansola7115]

Nothing spectacular , did it in college as typical

[@henryhampton4496]

That is a complete waste of time and so stupid you would never use that👎👎👎👎👎