# How do you solve 4log_4 (x) - 9log_x (4) = 0?

Mar 14, 2016

You must first simplify using the rule ${\log}_{a} m = \log \frac{m}{\log} a$

#### Explanation:

First, we must use the rule $a \log n = \log {n}^{a}$

${\log}_{4} \left({x}^{4}\right) - {\log}_{x} \left(262144\right) = 0$

$\frac{\log {x}^{4}}{\log 4} - \frac{\log 262144}{\log} x = 0$

Place on a common denominator.

$\frac{\log x \left(\log {x}^{4}\right)}{\log 4 \left(\log x\right)} - \frac{\log 4 \left(\log 262144\right)}{\log x \left(\log 4\right)} = 0$

Convert to exponential form.

${x}^{5} / 1048576 = {10}^{0}$

${x}^{5} = 1048576$

$x = \sqrt[5]{1048576}$

$x = 16$

Hopefully this helps!