# How do you simplify log_2(2^x)?

${\log}_{2} \left({2}^{x}\right) = x$
The logarithm ${\log}_{b}$ for any (meaningful) base $b$ is the inverse of the exponent using that base.
So ${\log}_{b} \left({b}^{x}\right) = x$ for any Real number $x$ and base $b > 0$ with $b \ne 1$