Question

how do you find the inverse of f(x) = 2^x

Answer 1

log_2 (x)

Answer 2

y=2^x

Answer 3

ln(y)=xln2

x=ln(y)/ln(2)

\[f^{-1}(x)=\ln(x)/\ln(2)\]

Answer 4

The inverse function for 2^x is log base 2 of x (log_2 (x)).

Answer 5

... which can be written in terms of other logarithms, like ln, by using log_2 (x) = ln(x) / ln(2), as in what .Sam. wrote, for example. But the simplest answer is log_2 (x).