Question

what is the inverse of the logarithmic function $f(x)=\log_{2}x$?
$f^{-1}(x)=\log_{x}2$
$f^{-1}(x)=x^{2}$
$f^{-1}(x)=2^{x}$
$f^{-1}(x)=\frac{1}{\log_{2}x}$

Explanation:

Step1: Set $y = f(x)$

$y = \log_{2} x$

Step2: Rewrite in exponential form

$x = 2^y$

Step3: Swap $x$ and $y$ for inverse

$y = 2^x$

Answer:

$\boldsymbol{f^{-1}(x) = 2^x}$