Question

What is the inverse of f(x)=2^x

Answer 1

`{f}^( - 1) (x) = (ln(x))/(ln(2))`

Explanation:

`f(x)=2^x`

`y = {2}^(x)`

`x = {2}^(y)`

`{2}^(y) = x`

`ln( {2}^(y) )=ln(x)`

`yln(2)=ln(x)`

`(yln(2))/(ln(2)) = (ln(x))/(ln(2))`

`y = (ln(x))/(ln(2))`

`{f}^( - 1) (x) = (ln(x))/(ln(2))`

Hope it is helpful...