# How do you solve log5^(2x) = 4?

Nov 4, 2015

The solution is $x = \frac{2}{\log} \left(5\right)$

#### Explanation:

A property of lohgarithms states that

$\log \left({a}^{b}\right) = b \log \left(a\right)$

In your case, $a = 5$ and $b = 2 x$, so the equality becomes

$\log \left({5}^{2 x}\right) = 2 x \log \left(5\right)$.

At this point, it's very easy to isolate the $x$, since $\log \left(5\right)$ is just a number, and we have

$\log \left({5}^{2 x}\right) = 4$

$\iff$

$2 x \log \left(5\right) = 4$

$\iff$

$x = \frac{4}{2 \log \left(5\right)} = \frac{2}{\log} \left(5\right)$