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

How to use logarithms to solve general exponential equations. Other techniques are also discussed.

[plutoh]

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

[luckn.]

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!

[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.

[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.

[fluffers]

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!

[amysmith]

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

[dildobaggins]

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...

[adrianmorales]

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..

[havaneseday]

Incredible!! Thank you Professor Leonard

[MATEMATICAalALCANCEdeTODOS]

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

[somebody]

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

[georgesadler]

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.

[mickeyp]

boy that problem at 50:00 is a beauty

edit: quickly superceded by 1:00:00. Wow. So goddamn elegant

[aidenvogt]

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.

[Squash]

this video especially towards the end killed me.

[Peter_]

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.

[mickeyp]

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

[dogwithwigwamz.]

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 ?
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 `.` .

[corsair]

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)

[anotheruser]

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.