# How do you solve Log 5x + log x^2 - log x = 5?

Nov 21, 2015

Elementary

Lets recall a few rules;

$\log a + \log b = \log a b$

$\log a - \log b = \log \left(\frac{a}{b}\right)$

Okay

$L o g 5 x + \log {x}^{2} - \log x = 5$
$L o g 5 {x}^{3} - \log x = 5$

$L o g \left(\frac{5 {x}^{3}}{x}\right) = 5$

$L o g 5 {x}^{2} = 5$

Now this is a base 10 logarithm

so ${10}^{5} = 5 {x}^{2}$

Solve and you shall get$x = \pm 100 \sqrt{2}$