Question

How do you find the inverse of `y = 2^x` and is it a function?

Answer 1

The inverse of `y=2^x` is `y=log_2 x`

Explanation:

This is how to do it.
From the given `y=2^x`

interchange the variables so that

`x=2^y`
then solve for y:

`x=2^y`

take the logarithm of both sides with base`=2`

`log_2 x=log_2 2^y`

`log_2 x=y`

and

`y=log_2 x`

The graph of `y=2^x` and its inverse `y=log_2 x`. They are symmetric with the line `y=x`

graph{(y-2^x)(y-log x/log 2)(y-x)=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.