# How do you solve log_3x=5?

Sep 30, 2016

$243$

#### Explanation:

Let's think about the meaning of the expression.

${\log}_{3} \left(x\right) = y$ means that, if I want to obtain $x$, I must raise the base $3$ to the $y$-th power.

In other words, $y$ must be the exponent that we must give to $3$ to obtain $x$, or again, ${3}^{y} = x$.

In our case, $y = 5$, so ${\log}_{3} \left(x\right) = 5$ means that $x$ is the number you obtain by raising $3$ to the fifth power, and so $x = {3}^{5}$. If you prefer, $x = 243$.