# WHat is x if 3log_2 (x+1) = 15?

Nov 10, 2015

$31$

#### Explanation:

$3 {\log}_{2} \left(x + 1\right) = 15$

...divide both sides by 3

${\log}_{2} \left(x + 1\right) = 5$

... apply ${2}^{a}$ on both sides in order to get rid of the ${\log}_{2}$

${2}^{{\log}_{2} \left(x + 1\right)} = {2}^{5}$

... use ${2}^{{\log}_{2} \left(a\right)} = a$ since the operations ${2}^{a}$ and ${\log}_{2} \left(a\right)$ are inverse

$x + 1 = {2}^{5}$

... take $1$ on both sides and simplify ....

$x = {2}^{5} - 1 = 32 - 1 = 31$