# How do you solve x=log_12 144?

Dec 2, 2015

$x = 2$

#### Explanation:

Even if there's nothing to "solve", strictly speaking, I assume you simply want to simplify ${\log}_{12} \left(144\right)$, and it's very simple:

${\log}_{a} \left(b\right) = x$ means that $x$ is the exponent that you must give to $a$ to obtain $b$. Namely: ${a}^{x} = b$.

This means that, in your case, ${\log}_{12} \left(144\right)$ is the exponent that you must give to $12$ to obtain $144$, and since $144 = {12}^{2}$, that exponent is $2$. So,

$x = {\log}_{12} \left(144\right) = 2$