# How do you solve ln(x-2)^2=6?

Aug 15, 2016

We will solve for $x$ using the very basic properties of natural logarithms. I'll illustrate it below.

#### Explanation:

We have, $L n {\left(x - 2\right)}^{2} = 6$

Using the property, $L n {m}^{n} = n L n m$,

We have, $L n {\left(x - 2\right)}^{2} = 6$

$\implies 2 L n \left(x - 2\right) = 6$
$\implies L n \left(x - 2\right) = 3$
$\implies x - 2 = {e}^{3}$

In the last step, we used the concept of inverse of the natural logarithms, $L n m = n \implies m = {e}^{n}$

Thus,$x = {e}^{3} + 2$

Where $e$ is the base of natural logarithms.