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

Jul 2, 2016

The solution is $x = e$.

#### Explanation:

First you apply the rule of the log for the powers

$\ln \left({x}^{k}\right) = k \ln \left(x\right)$ then, for you it is

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

$2 \ln \left(x\right) = 2$

$\ln \left(x\right) = 1$.

Then, to obtain $x$ you need to apply the inverse operation of $\ln$ that is the exponential

${e}^{\ln} \left(x\right) = {e}^{1}$

$x = e$.