# Thread: How do i find the inverse of Log functions???

1. ## How do i find the inverse of Log functions???

Hi!!

Im trying to teach myself how to do the inverse of ln functions, so most of what I know is only from my book :P

So this is the question,

f(x) = 2ln[(x^2)/3]+ 3

the thing is how do i get the inverse of ln? do i multiply it by 'e' if the inverse of 'e' is ln 'e'?

Thanks@!

2. Originally Posted by appleseed
Hi!!

Im trying to teach myself how to do the inverse of ln functions, so most of what I know is only from my book :P

So this is the question,

the thing is how do i get the inverse of ln? do i multiply it by 'e' if the inverse of 'e' is ln 'e'?

Thanks@!

The inverse of $\displaystyle \ln(x)$ is $\displaystyle e^x$ but only for $\displaystyle x>0$. This is because the log of a negative number is undefined.

More generally if $\displaystyle f(x) = \log_b(x) \: , b \neq 0,1 \: , \: x >0 \text{ then } f^{-1}(x) = b^x$

3. Originally Posted by appleseed
Hi!!

Im trying to teach myself how to do the inverse of ln functions, so most of what I know is only from my book :P

So this is the question,

the thing is how do i get the inverse of ln? do i multiply it by 'e' if the inverse of 'e' is ln 'e'?

Thanks@!
There are two things wrong with this- you do not "multiply" by anything, you take the exponential function- that is e to that power.

Also it makes no sense to say "the inverse of 'e' is ln 'e'". "e" is a number, not a function. The inverse of the function $\displaystyle exp(x)= e^x$ is ln(x) and so the inverse function of ln(x) is $\displaystyle e^x$:

$\displaystyle e^{ln(x)}= x$ and $\displaystyle ln(e^x)= x$.