Solving Exponential Equations with Logarithms (Precalculus - College Algebra 64)

[@plutoh28]

Done with the log series! 1 step readier for calc 1 in 2 weeks

[@Wealthy_ishhh]

You're the greatest thing that has ever happened to youtube never stop uploading, you have saved me you are the reason I'm passing the class.

[@luckn.3371]

Would just like to say, i appreciate all that you've done for us students, and even continuing to post videos throughout the years into quarantine what with all that you've gone through. Thank you and God Bless!

[@havaneseday]

Incredible!! Thank you Professor Leonard

[@fluffers7997]

Your videos are helping me so much. I've been restudying things on my own in prep to go back for a physics degree after dropping out years ago. I knew HOW to do this stuff, but never cared about the WHY which lead to knowledge holes that made me feel inadequate in upper level classes. The textbooks I picked up just say "do it like this" instead of explaining why it's better to use ln over log. Brute force memorization is what got me into this predicament. I actually want to fully understand what I'm doing not simply know enough to pass a test. You're truly saving me so much time and headaches while setting me up for success!

[@amysmith7508]

I found this video INCREDIBLY helpful!! Thank you so much for sharing this.

[@thedebis]

From a phobia whenever I saw a ln(x) to having fun double checking my work, thank you so much for dedicating so much time and patience creating this high quality curriculum. This lecture series has undone such a bad education system I went through.

[@dildobaggins2759]

Just want to say hope youre doing well professor Leonard and may all the luck in the world come your way to keep you safe and happy so you can carry on doing what your doing...

[@elguigomafla]

above and beyond.thank you

[@somebody401]

Fantastic way of explaining and simplifying concepts. Thank you, Professor Leonard.

[@georgesadler7830]

Professor Leonard, thank you for another exceptional video/lecture on Solving Exponential Equations with Logarithms. All the analytical and problem-solving tools are needed to solve Exponential and Logarithmic problems in Precalculus/College Algebra.

[@aidenvogt7036]

Hi Professor, huge fan of your videos (You got me through multi variable calculus). I wanted to ask if you’d be willing to make a video (or videos) on harmonic Oscillators in the calculus sense, as well as the method of Undetermined Coefficients. Big fan, keep it up.

[@adrianmorales3879]

39:58 this is the absolute best smoulder ive seen in my life haha. Not even going to complain about it LMFAOOOO. I need this guys intelligence and charm..

[@MatematicaPaP]

30:49 "... compose a function with its inverse ..." 39:44 "... exponential's range is from zero to infinite, that matches perfectly with the domain of a logarithm being zero to infinity that we need to use a logarithm anyhow. That's why this technique works, they are inverses on their respective domains." 39:58 SUBSTITUTION

[@emmers810]

thanks so much, I loved this lesson

[@Squash101]

this video especially towards the end killed me.

[@mickeyp6639]

boy that problem at 50:00 is a beauty edit: quickly superceded by 1:00:00. Wow. So goddamn elegant

[@Peter_1986]

The fact that logarithms can sort of turn multiplication into addition is actually one major reason why Bode plots are drawn in logarithmic form; because this makes it much easier to combine different graphs together into one single plot, since you can simply add them together.

[@mickeyp6639]

I was really confused because at 37:00 I moved the x instead of the 3 over to the other side because I hate negatives and then factored it out and then divided out the (lnpi-1) to get a result of 3/(lnpi-1) and was like wtf theres no way thats the same result as Leonard's answer of -3/(1-lnpi) and was trying to figure out how what seemed like an obviously viable just different way to do it gave such a different answer. Checked them out on symbolab and they are equivalent. Wild how varied math gets at this level, can't wait for it to just get more wild edit: Actually upon rereading I see how that works. the lnpi is just larger than 1 so when subtracted becomes negative and turns the whole fraction positive. F***ing cool stuff bruh

[@corsair438]

6th method for ex 1: 8 3^(x+1) = 5 ; 8 ∙ 3 ∙ 3^x = 5 ; 3^x = 5/24 ; x = log3 (5/24) ; x = log (5/24)/log (3)

[@dogwithwigwamz.7320]

There`s a problem here which many tutors of maths seem to find trivial - and have dismissed when I raise the problem with them. It is this : Looking at that first equation in this video I thought to write it down and attempt to solve it. But do I write 8.3..., or 8x3..... ? The `modern` fashion seems to be to replace the `command to multiply ( x ) with what looks like a decimal point. I presume this was to avoid the command to multiply being confused with the variable `x` in common use - but it actually only confuses things further. I thought that if maths means anything it means precision. Suppose I hand wrote the answers to a maths paper and not once used the `x` as a command to multiply but instead `.` .

[@narendratella712]

Nice sir.

[@antonludwigaugustvonmacken8680]

Professor Leonard, will you ever do a numerical methods series?

[@anotheruser9876]

At around 4 minutes in I would have kept the 5/8 and (X+1) on the same side of the equal sign as in the equation before. The switch is a bit confusing.

[@chriscunningham177]

are the change of base properties intuitively useful without the existence of an electronic calculator? it seems to be a system derived because some more primitive calculators were unable to handle a base other than 10 or e. Also: what does a constant in front of the variable do to points on a graph? ie: for 'log Cx', what does the C do? i was able to glean from back of the book solutions that it to divides the x by C. is this accurate?

[@anis1930]

what can we do in the case where instead of having 2^(x) + 2^(x+2) - 12 = 0 we had 2^(x) + 7^(x+2) - 12 = 0 so when the exponents are not the same and we cant simplify one into the other .

[@HamzaKhan-go6wr]

Sir could I ask when this course will be over I want to download all the videos at once because I want to finish the course in a specific time so I should know how many hours and days and weeks it will take so please.. Thank you

[@cienciamulticultural3489]

Hi, does anybody know on what lesson did he teach about the cross with wich he finds the numbers for the binomium? thanks

[@shravans7184]

Quadratics -part (ax^2+bx+c=0)

[@isabelleambrose9293]

i feel like an imposter in my own class god i really need to reevalute my life choices

[@thedebis]

No you're watching Lecture 64 ... of a 73 episode series, has nothing to do with your abilities lol. You're jumping into the 6th season of a 10 episode per series show and blaming yourself for not understanding what's happening. Lol you gotta binge the the earlier episodes. You got this!!!

[@shravans7184]

@51:00I thought 2.49 ^x and 11.7^x and pause the video ........wasted 20 minutes, gave up and Resumed the video again and found that what Professor meant was 2x 49 ^x and 11 x 7^x........ if it was expressed it in that form I would have saved my 20 minutes.......

[@srinathb4742]

what is log((2^x)+1) can anyone help?

[@lasranasmalevolas3303]

7:38

[@tasfiaahsan6262]

❤️❤️❤️

[@Alex-jo2oi]

😵‍💫

[@AdnanKhan-mm6bo]

1st..✋❤

[@nixongravity283]

🙃

[@ryanstevens2722]

As always Mr Brandon shows his superior math knowledge. However, for a student seeing this for the first time versus his 20 years of math education and instructing, he is very confusing with his very fast speech pattern. He seems to be speeding up his lectures from earlier ones I've watched. Just asking if he could pace these better for folks seeing the info for the first time and trying to follow ans understand it all.

[@brookefoor6265]

I'm not sure if this will help- but youtube allows the option for slowing down the video. I actually speed up most of his videos because I have so little time. If it weren't for him I'd be failing statistics.

[@ProfessorLeonard]

Hi Ryan! Firstly, thanks for watching and for commenting. It's always appreciated. I absolutely understand where you are coming from in regard to the speed at which this is covered. However, this is should be the second chance at exposure to this material in the math sequence, and this is the case in my channel as well. The concept of exponentials, logarithms, and solving equations involving them is first introduced in Intermediate Algebra (the previous course/playlist). I always direct students to view that first because it is covered in-depth and introduced so that students with limited exposure can learn the material. Here is a link to the playlist where this material is first introduced. Exponentials themselves are discussed in unit 12. I hope that this helps as I know first-hand what it's like to try to learn something but the material seems too fast. Please let me know if you find this playlist helpful and thanks again for watching!

[@veryhealthy9962]

Im surprised to see this comment because I felt exactly this since the 50th video or so. I had to watch in 0.75 or 0.65 to listen in a manner where I could absorb what he was saying. Granted I could be a slow listener, but the speech rate has been increasing from video to video

[@nixongravity283]

3rd liker 🙃

[@AdnanKhan-mm6bo]

👍