# How do you simplify 2^(log_2(12)) ?

Mar 17, 2016

${2}^{{\log}_{2} \left(12\right)} = 12$

#### Explanation:

By definition, the base-$a$ log of a number $x$ is the value $y$ such that ${a}^{y} = x$. That is to say

${\log}_{a} \left(x\right) = y \iff {a}^{y} = x$

Then, applying the definition, for any $a$, we have ${a}^{{\log}_{a} \left(x\right)} = x$

In this case, that gives us ${2}^{{\log}_{2} \left(12\right)} = 12$