# How do you simplify 2log_5 12-log_5 8-2log_5 3?

Nov 10, 2016

This simplifies to ${\log}_{5} \left(2\right)$.

#### Explanation:

Use the rule $a \log n = \log {n}^{a}$ to get rid of the coefficients.

$\implies {\log}_{5} \left(144\right) - {\log}_{5} \left(8\right) - {\log}_{5} \left(9\right)$

Next, use the rule ${\log}_{a} \left(n\right) - {\log}_{a} \left(m\right) = {\log}_{a} \left(\frac{n}{m}\right)$.

$\implies {\log}_{5} \left(\frac{\frac{144}{8}}{9}\right)$

$\implies {\log}_{5} \left(2\right)$

Hopefully this helps!