# How do you solve for x in log10^(x^2)=4?

Jan 13, 2016

$\log \left(x\right)$ and ${10}^{x}$ are inverse functions, hence ${x}^{2} = 4$ so $x = \pm 2$.

#### Explanation:

As Real valued functions, $\log \left(x\right)$ and ${10}^{x}$ are inverses of one another.

So:

$4 = \log \left({10}^{{x}^{2}}\right) = {x}^{2}$

Hence $x = \pm 2$