Comparing exponential and logarithmic functions | Algebra II | Khan Academy

Missed the previous lesson?

Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to Khan Academy’s Algebra II channel:

[tidus]

very useful stuff, we are just starting to go through graphs and logarithms, these videos are helping quite a lot! thanks a lot sal! :)

[metallerever]

Khan you are my hero and my saviour, i learned so much things about EVERYTHING with your videos

[nobody]

log is the inverse of the exponent relating to y=x, assuming the bases of both are the same.

i.e. y=log(x)^z is inverse (relative to x=y) to y=x^z

logarithms increase asymptotically to the x, while exponents increase asymptotically to the y.
if you want big y numbers use exponents, not logs. got it.

[SilverAura]

The moment you said "REFLECTION" was the moment I instantly had a word for what I was trying to express. This entire time, I absolutely knew logarithmic and exponential were related, but saying they were opposites didn't feel appropriate. I knew at some level they were opposites, but seriously... that word "reflection" was the moment it all clicked for me. Absolutely beautiful video, thank you so much!

[TheTapion]

so I'm assuming this is why you have to tack on a ln(of the base) when taking the derivative of a exponential function raised to a function.

[babbelfisch]

i realy love your videos keep on going like you do :)

[alexgalan]

Which is the name of software you use?

[heatherstein]

Did I miss it? Does this mean y is porportional to x^2?

[matthewneryaev]

Am i the only one trying to figure out how he writing so nicely with a mouse?

[PdjBestBuyCnc]

You need to quit, quit, you got to quit repeating, repeating yourself so much, stop repeating yourself so much. This makes the videos very hard to listen to. If I do not get something I would rather rewind than hear you repeat so much!