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

Dec 2, 2015

Apply the exponential function and use a property of logarithms to find that
$x = \pm e$

#### Explanation:

For this problem, we will use that
${e}^{\log} \left(a\right) = a$

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

$\implies {e}^{\log} \left({x}^{2}\right) = {e}^{2}$

$\implies {x}^{2} = {e}^{2}$

$\implies \sqrt{{x}^{2}} = \sqrt{{e}^{2}}$

$\implies | x | = e$

$\implies x = \pm e$