Evaluate and Graph Logarithms (Part 3)

What are logarithms? Why do we need logarithms? They undo exponentials. They're inverse functions. Part 1: logarithms are defined, and a number examples of moving between logarithm form and exponential form are shown. The common log (base 10) and natural log (base e) is explained, followed by the change of base formula. Part 2: How to evaluate logs (logarithms) without a calculator by changing it into exponential form, and examples of why logarithms and exponential functions being inverses helps in simplifying expressions. Part 3: Beginning with a review of exponential graphs, logarithms are explored as inverses (everything that was x becomes y and everything that was y becomes x). Horizontal asymptotes are now vertical asymptotes and y-intercepts are now x-intercepts. This is followed by transforming those basic graphs.

[RichardGoans]

I have to say I felt hopeless after my last College Algebra class and then I found your videos. I really want to say thanks man you have turned it around for me.

[pammazolaXP]

I never thought I'd say this about algebra, but I enjoy watching these videos. Thanks!

[nikkibbean]

Super helpful substitute for my incompetent teacher. Thanks so

[BarelyPerfect]

Thank you so much for posting these online sir!

[davidtutorsmath]

@870Juggalo You are very welcome. Thanks for taking the time to appreciate, and good luck as you finish up with college algebra.

[davidtutorsmath]

@Willowheart4321 You're quite welcome. When you have y=log(2x), it messes with it horizontally (because it's with x). Also, because it's with the x, it does it in the opposite way of what we think - multiplying by 2 actually causes a HORIZONTAL SHRINK, just like log(x+2) would shift the whole graph (asymptote and all) to the LEFT 2 even though my brain thinks +2 should be to the right. Plot some points or use a graphing calculator to see what I mean. All points get closer to the asymptote.

[dolphingirl]

thank you so much for actually explaining these things, something my teacher never bothered to do ;_;

[davidtutorsmath]

@colorfulpride Thanks. I'm glad it helped. Good luck as you continue to work with logarithms.

[davidtutorsmath]

@pammazolaXP Awesome! Isn't it great when you finally understand something? Keep asking questions and searching for answers. Math really is logical. You're welcome. I'm glad you enjoy the videos.

[davidtutorsmath]

@nikkibbean Glad you found it helpful. Give your teacher some credit, though. Ask him/her questions to be able to clarify. Don't write them off as incompetent.

[davidtutorsmath]

@mamba4590 Thanks for appreciating. Glad it helped.

[Willowheart]

Thank you! Only one thing, what happens when there is a number that multiplies x? ex: f(x)=log 2x