# Math Help - Logarithm Equation

1. ## Logarithm Equation

How do you solve this? I'm confused.

$(\log x)^2 = \log x^2$

2. Originally Posted by JSB1917
How do you solve this? I'm confused.

$(\log x)^2 = \log x^2$
$(log(x))^2 - 2log(x) = 0$

This is now a quadratic in log(x) which can be solved like any other quadratic but remember the domain restriction on log terms:

hint: let $u = log(x)$

Spoiler:
$log(x)(log(x)-2) = 0$

$log(x) = 0$ (which can be discounted since we can't take the log of 0)

$log(x) = 2$

$
x = 10^2 = 100$