How do you solve 15+2log_2x=31?

Sep 7, 2016

$x = 256$

Explanation:

We have: $15 + 2 {\log}_{2} \left(x\right) = 31$

First, let's subtract $15$ from both sides of the equation:

$\implies 2 {\log}_{2} \left(x\right) = 16$

Then, let's divide both sides by $2$:

$\implies {\log}_{2} \left(x\right) = 8$

Now, using the laws of logarithms:

$\implies x = {2}^{8}$

$\implies x = 256$

Therefore, the solution to the equation is $x = 256$.

Sep 7, 2016

$x = 256$

Explanation:

$15 + 2 {\log}_{2} x = 31$

$\Leftrightarrow 2 {\log}_{2} x = 31 - 15 = 16$ or

${\log}_{2} = 8$

Hence $x = {2}^{8} = 256$