# How do you solve for x?: log_2(2^(x+3))=15?

Oct 21, 2015

$x = 12$

#### Explanation:

${\log}_{2} \left({2}^{x + 3}\right) = 15 \implies$ if ${\log}_{a} \left(x\right) = y \Leftrightarrow x = {a}^{y}$ , so:

${2}^{x + 3} = {2}^{15} \implies$when the same bases to different exponents are

equal then the exponents must be equal, then:

$x + 3 = 15 \implies$ subtract 3 from both sides:

$x = 12$