# How do you solve 2 log x^4 = 16?

Feb 19, 2015

It depends upon the base of your logarithm. Let us assume that the base is a number $a$.

You have:

$2 {\log}_{a} {x}^{4} = 16$

${\log}_{a} {x}^{4} = \frac{16}{2}$ the power of $4$ can go as multiplier of log:

$4 {\log}_{a} x = 8$ and again:

${\log}_{a} x = \frac{8}{4}$

${\log}_{a} x = 2$

$x = {a}^{2}$

Now, you can choose the value of $a$. Normally (when it is not specified) it should be $10$, so if this is the case you get:
$x = {10}^{2} = 100$