Solving Logarithmic Equations with Exponentials (Precalculus - College Algebra 63)

[@carlosgerman9999]

I hope he keeps going at this pace with these videos! Love it! We're getting close to trigonometry I believe? PLEASE DONT STOP THIS PLAYLIST!

[@georgesadler7830]

Professor Leonard, thank you for a monster and mammoth lecture/video on Solving Logarithmic Equations with Exponentials. The analytical solutions and the changing of bases increase my knowledge of the subject. Students should do massive number of problems for a solid understanding of the subject.

[@tasfiaahsan6262]

Logarithm finished... Waiting for the next one Professor ❤️

[@ayrthhhn]

The last two examples were mesmerizing, very neat stuff comes up when dealing with these log equations!! Thank you Prof!

[@creativecloudaddict]

i love you for uploading this. you have no idea how helpful this is. thank you so much.

[@TheDominion37]

Very good lecture. Providing multiple explanations really demonstrates a thorough process of how to visualize each example.

[@greateditz795]

Professor Leonard, your videos are very helpful. Your teaching method is so good and easy to understand.

[@maryhowell5753]

Thanks for the video Professor!

[@danielrosario.santos]

Thank you for this awesome video!

[@rosepierce9382]

Congrats on 704K, Professor!🎈

[@Boognish64]

12 years after I passed my last math class in college out of my professor's pity -she thought I was suicidal at the time and the section on logs dropped my grade from a B minus to a D minus- I come back and watch this series. As I try to keep up, follow the well explained logic and practice the examples I conclude: Yeah. I'm just bad at this. Luckily it's never come up outside the classroom

[@rozha3963]

thank you professor THANK YOU!!!!

[@endinakojikeleza]

Best lecturer

[@ltac8194]

Legend is correct. Also GOAT ( i just learned what that meant during the super bowl). Any who, thanks for making Maths fun.

[@sergeydukman5832]

Thanks a lot. Keep going

[@reembaz7929]

thank you soo much, you have helped me a lot

[@johnbui5822]

legend

[@veryhealthy9962]

I feel as if I 'dropped' out of class from 36:00 onwards. The last 3 examples were hard that I started to question myself (Because the earlier examples for the past few videos were easy)

[@mathshortway]

Excellent.

[@johnhebert7445]

I would love a video or series of videos discussing extraneous solutions in more detail (i.e., 16:45). From what I understand the root cause of them are performing irreversible operations when solving equations like squaring for example. Apparently they can also come into play when multiplying or dividing both sides of a solution by x since there is a possibility that x could be zero. Solving absolute value equations can result in extraneous solutions as well. The idea of no solution, multiple solutions, or unique solution in linear systems is also this same type of idea. Is there a parallel to this for nonlinear systems? Domains, ranges, all of these types of things I would like to be much more comfortable with and not always have in the back of my mind when working with math.

[@eobardrush2112]

Hello Professor Leonard. Thanks for the lectures as always! These really help I have a question tho. When will we get to Trigonometry?

[@guidofeliz8384]

Trig is coming soon.

[@gauravkumar-hr3de]

Sir please teach antilogarithms

[@eugenepashch5213]

Great!

[@masulekachingo1064]

why did you divide by on 31:00(Time)

[@guidofeliz8384]

What about applications involving exponential and log function?

[@endinakojikeleza]

Proffesor may you please solve for me this question 2 to the power of logx = 2x

[@timothysantiago425]

AT LOG LOG [2X+1/X-2] = 1 SUPPOSE TO HAVE PARENTHESIS FOR PROBLEM # 2

[@somasahu1234]

EASY - eer!

[@billzemon8628]

Possible error?? 2(log4 x)^2 + 3log8 x = log2 16 in the fourth line of the solution you changed the denominator of the first element from 2 to 4. I believe the solution 1/16 is not correct.

[@rosepierce9382]

In the last example, couldn't we have changed the base to 2 or 6? Why 'ln'?

[@Wumbology10]

Because you have to think of it as an exponential form too. Base 2 to the exponent 6 does not equal 6 and vice versa; therefore it's best to use log base 10 or ln.

[@lseansiamz4251]

I wish he teaches physics

[@JM-ww7ou]

this is where math starts to get super fcked up. good lord that last problem

[@TheGreat8220]

Is the X he drew some way to help determine factors? I don't understand why he wrote it that way. (@ 23 min mark)

[@mickeyp6639]

did you watch the beginning of the series? It's a shortcut for factoring quadratics. I would recommend you go either to the beginning of the series or check out the factoring lecture in intermediate algebra series for more detail

[@The_Angry_BeEconomist]

lol @ I don't really want to 22:24

[@lasranasmalevolas3303]

16:40

[@somasahu1234]

Hit the like button if u want more tough questions !!!

[@tamarapinto1720]

*_Here from TikTok_*

[@Nannanono]

Literally me a few mins agoo

[@tamarapinto1720]

_😅_

[@rosepierce9382]

54:37 Kinda scary.

[@may8128]

man I got lost at 51:34 =( nevermind I get it

[@HansensUniverseT-A]

I feel truly sorry for the poor bastards having to do this at school glad i am done and over with this misery.

[@eobardrush2112]

I am done with school too but maths is my passion so I have been learning maths on my own even after school because its so interesting. Most of the people in school hates math because they dont understand it

[@guidofeliz8384]

I am 55 and decided to revisit math learned long ago. I am far from misery.

[@waseemq1522]

@@eobardrush2112 IKR , PEOPLE JUST HATE MATH BECAUSE THEY DON'Y KNOW WHAT'S GOING ON.

[@Peter_1986]

@@waseemq1522 Math is frequently poorly taught, and a lot of people lose interest in math because they get too few examples of real-life applications. Also, math is a very cumulative type of subject, so you cannot just "kind of" pass one course and then suddenly ace the course after that - you need to regularly review old stuff, and make sure that you don't forget some of the really important stuff. Of course, sometimes you can review old courses through more recent courses - like for example if you can find tangent planes, then you can obviously find tangent lines - so sometimes you can cover as much as possible about one concept by practising more general situations.

[@endinakojikeleza]

Best lecturer

[@endinakojikeleza]

Best lecturer

[@endinakojikeleza]

Best lecturer

[@endinakojikeleza]

Best lecturer

[@endinakojikeleza]

Best lecturer