❖ Solving Exponential Equations - Three Basic Examples ❖

Solving Exponential Equations - How to Solve for 'x' When It's an Exponent
In this video, I show how to solve for x when it appears as an exponent in an exponential equation. We go through a few different cases to cover the most common methods for solving these types of equations.
For the first exponential equation, we use the method of like bases to simplify and solve for x.
The second and third examples can’t be solved with like bases, so instead we use the natural logarithm function (LN). I demonstrate how to apply logarithmic properties to solve the resulting equations step-by-step.
This video is perfect for students learning about exponential equations and logarithms, as well as those needing a quick review on how to use logarithms to solve equations.
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#ExponentialEquations #SolvingExponents #NaturalLogarithm #Logarithms #MathTutorial #Algebra #ExponentialFunctions #LearningMath #MathHelp #Mathematics

[@patrickjmt]

If you LIKE the video please thumbs up and leave a comment! I'd appreciate it :)

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Uploaded 10 years ago. Still helping people like me getting through exponents easier. You deserve way more views for this simple but helpful video.

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Yeps!

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Knowing that some of you guys do this in college gives me hope that It's not too late to catch up in maths

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Im doing this in 7th grade

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Nina Torees funny coz we never get this kinda of questions, but you come this as you working towards the solution... it’ll to your advantage to know this before you get to college...

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STOP LYING, Im in a AP program and seeing this in grade 10 lmao

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in the uk they do this in year 7 what with the new 9-1 its in the syllabus now......

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I think you are seriously one of the best math teachers I have ever had! It takes me 40 minutes to understand my teacher, only 10 to understand you! Thank you so much :)

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How did they go?

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In fact, most of the teachers can't explain math well.

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Fr lol

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I wish math teachers could explain things so easily, great video!!

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God bless you, I just cant see why my teachers explanations are not so smooth and simple. Another thing I like about the way you teach is that you go over more than one type of example.

[@jakeb8493]

Before this video, I had no idea what the "ln" thing was, but after watching this, I fully understand it. Thank you SO much!

[@thefrankbros1130]

You my friend, have my deepest and upmost thanks for this video

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Thank you so much for this, think I've learnt more here than in 2 hours of class

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+Priscilla Terriquez Pleasure

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hi darling you understood then you teach me

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Your work is neat and I wish all math teachers were as easy to understand. Everyone needs to subscribe to you. Keep up the great work!

[@patrickjmt]

you are very welcome!

[@patrickjmt]

glad i could help :)

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YOU HELPED ME ALT THANKS!!!

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the world needs alot of people like you,thanks for being a great human.

[@jopeezy6971]

Thank you so much, hours of class time with a hard to follow professor left me confused. However after 6 minutes of you explaining this has given me the comprehension and confidence needed to pass my test tomorrow. Keep it up man, you deserve the 30$ an hour my professor gets!

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Hey man its people like you that keep me from failing college thank you for posting these vids. I highly encourage people to keep posting info videos. They just really help everyone out. keep up the good work my friend!

[@lovestein55]

taking a summer mathematical modeling class that's two and a half hours long and you explained this better in 7 mins than my professor has the entire two months lmao

[@MsTD1995]

I have been looking for help on YT for a week now!!!! thank you!!! that looks so simple when you do it. you saved me!! :)

[@ceeboi2092]

Thanks for the refresher, it's been about 18 years since I used logs this video is a huge help! Thanks!!!

[@patrickjmt]

@theninjadang my pleasure : )

[@laughs2go1]

You're amazing! I don't know how you do it but you explain it in a way that doesn't confuse me at all.

[@younglife88]

THANK YOU SO MUCH ,for your simplicity and step by step instructions.

[@imperviousfatality]

Why are you so awesome!! My teacher fails at teaching, but you are saving my life (:

[@Genesis3338]

Thank you for making these videos available and simple enough for people who have been cursed with less than average math teachers! You have awesome handwriting to be left-handed, by the way! :D

[@ninjapirate123]

are u still alive

[@happinessrunns]

Your last example saved my life, I was looking everywhere for an explanation for that type of equation. Thank you!

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[@happinessrunns]

@@ninjapirate123 yeah, lol. I remember when this was hard.

[@ninjapirate123]

@@happinessrunns Now since you've gotten older u find this very easy

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​@@happinessrunnsu still alive in the year 2024?

[@maribnsaad]

Great ideas mr. Patrick. I wanna thank you so much for these videos. It helps me a lot. you are the teacher I've lost.

[@xadeayox]

Thanks for the explanation. I'm really grateful for all your efforts and the explanation was excellent. I was able to learn and understand some things

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Thanks for the help man. Very generous. You seem to have a video for all my math problem needs

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super clear & helpful!! thanks again.

[@patrickjmt]

@bryfryable didnt rewatch but my guess is: no

[@SahajSoldier]

I should get a refund for my tuition and send it to you, you've taught me much more than my professor.

[@PortablePuertoRican]

Thanks You!!! I was stuck on a problem on my take home practice final and all the onther sites i went to always stopped the exponent lessons at what you did for question B. But you reminded me of the one thing I'd forgotten about, distributing after pulling the exponent in front. -_- I don't know why i keep forgetting that, but now i can take my Algebra final this week with a little more confidence. Keep up the Vids Dood! They are easy to understand and since i can pause I can take them at my own pace. They have helped me study for my final far better than simply doing problems over a over again ever could. :D

[@rmartini8001]

Thank you so much for making your videos. This is one of the best explanations I have gotten in math.

[@Guineapig108]

Thank you so much! This was thousands of times more understandable than what my teacher showed me. :D

[@maizeandblueheart]

Thank you! Your second example helped me a lot.

[@loballa246]

You are ten times better than my math teacher, I feel like I should pay you!

[@potatodude77]

thank you so much. i couldn't find how to do the last example anywhere on the internet or my textbook. you just saved me hours of frustration!

[@o0aDr0o]

nearing finals week, your videos have helped a bunch! thank you =D

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I haven't taken math in over a decade and now i'm in business calc trying to brush off some hardcore rust. You are a life saver!

[@patrickjmt]

happy to help :)

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Thanks you 👌

[@RepaidChalice37]

This was very helpful! I'm in a junior math class and I want to be a chapter a head we are doing ln next unit but it's so much easier to find answers to exponentially this way than to plug in random numbers or go to the graphing calculator

[@GabrielSavageMusic]

Have you got any videos of examples of how to go about solving more advanced exponential/logarithmic problems? One I'm struggling with right now is "4x^3 * e^-3x - 3x^4 * e^-3x" - Any suggestions?

[@badboyj7]

dog i love.....been using these vids for 2 years now ...good bless you for helpin everyone help like this!

[@patrickjmt]

glad i could help :) come back any time!

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im in 8th grade.. and this is tough, im glad you helped me. you just won yourself a new subscriber :)

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@MrCapeVerde the amount of work to understand intermediate algebra is rewarding. i had to take it a couple of times to let the material sink in. i'm glad that i did, because it built a strong foundation when i took calculus. once the math clicks in your head, you'll enjoy the material a lot more. that goes to any subject once you understand it. and i agree, it takes a lot of time, but it's worth the "eureka!" moment. :)

[@patrickjmt]

thanks for the kind words ;)

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Awesome Explanation! Clear as the Spring sky! You Rock! I don't understand how come some people don't like this video?

[@patrickjmt]

@DudeUForgotAmmo no, although i did have one paper published!

[@theolynwarrender]

Great video! Simple and straight to the point and well explained. Thanks man!

[@XavAskan]

Thanks you just saved my life on my quiz tomorrow. Well I could only see the first problem done before getting confused by logarithms. If that's how you spell it. Anyway first problem is probably still sort of advanced, but I'm a high school freshman that's been in high school only for a few weeks... Anyway thanks for the help!

[@Nikifuj908]

@patrickJMT For the example 2, would it make it faster just to take the log base 8 of both sides as the first step?

[@MegaBigfatbob]

The best! Ty, always very helpful and very clear explanation :)

[@paulnjeru2005]

Just realized that this is a ten year old video. Thank you for the great explanation of how to solve exponents with different bases in different scenarios. also realized that your also left-handed.

[@patrickjmt]

You're very welcome!

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Lean & simple. Thanks!!! Helped me a lot!!!

[@alexandriacastaneda3966]

Logarithmic properties allow you to do that. Add and Multiply result in the same number. Subtract and divide also result in the same number. review your Log rules:)

[@dhashennaidu6116]

Damn this was clear and concise. I literally needed to solve one problem and this was perfect.

Very long time since I studied math, 20+ years, but in 01:20 how do one know that can be done in the first place?

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its been 7 years and this is still saving grades thank you!

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This really helped a lot! Thank you so much!

[@patrickjmt]

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[@davidvalyo6288]

Thank you for an excellent video on how to do these exponent problem . Learned a lot.

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Thank you...so much...I don't know how to express this! My teacher takes the whole class speeding through the whole process and makes no sense to me-.-. Once again thank you so much sir!

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Hey...you are great! You have helped me numerous times. However, how do you get 24/5 and not 34/5 in the end? If you're adding, it is 34/5

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[@effie2857]

Hey, probably a daft question, but why can you multiply the ln4/5 and ln/6 just because they're being added together? Oh, and thanks for the video!

[@oZqdiac]

Because in logarithm rules log(a) + log(b) = log(ab) So basically when you add logarithms together you can multiply the two numbers in the logarithms together and make one logarithm with the product of those numbers. Also works for subtraction as well log(a) - log(b) = log(a/b)

[@kennethgoldberg83]

If you need a decimal approximation please make sure that the ln 6 is entered ln(6). The calculator will provide the left parenthesis. We need the right one in the right place so that the calculator will know what the argument is.

[@tim.e.l]

Thanks for the reminder. I completely forgot that you could just pull out the exponent when its in a log. I needed to calculate the number of rounds a tournament would have programatically and it is 2^x = y; where y is the number of teams. so x = ln(y)/ln(2). For 16 teams ln(16)/ln(2) = 4. Perfect!

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Savin my a$$ with each video u make. Thanks so much and keep up the great work

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My teacher took an entire half hour to explain the FIRST part of the question and no one understood it, i came home, watched this and boom, understood it in 2 minutes, AMAZING!!!

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The examples here help a lot for review. Thanks!

[@ExcelTutorials1]

very helpful. its been a while since I have looked at this. Thank you

[@christinekincaiddewey4791]

In example a, if you take log (base 3) of both side of the equation after you have converted both sides to base 3. Since logs are exponents, you are just left with the exponents equal to each other.

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Very good vid

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where are you watching from

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Very nice examples, thank you 🙏

[@abdulyoutub]

hi sir your method of teaching is fantastac and with patient, The only thing i suggest you please don't skip some step during writing because in this lesson i followed log and exponential very well but unfortunitly I was lost near to the end where you skiped 14 to divid etc without mentioning. for new learner it is hard to understand unless to see everything step by step. After all appreciat your hard work. In deed your help in website is a charity for those who wants to learn

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When am I gonna need this in real life

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why can you?

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I needed help with an equation like #2; thank you so very much!

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Thank you so much for existing