# How do you simplify  log_(5) (1/15)?

Jun 12, 2016

$= {\log}_{5} \left(1\right) - {\log}_{5} \left(15\right)$

Consider that $\log \left(1\right)$ of anything is equal to $0$.

$= 0 - {\log}_{5} \left(15\right)$

$= - {\log}_{5} \left(5 \times 3\right)$

Recall that $\log \left(a \times n\right) = \log a + \log n$

$= - \left({\log}_{5} \left(5\right) + {\log}_{5} \left(3\right)\right)$

Finally, remember that ${\log}_{a} \left(a\right) = 1$.

$= - {\log}_{5} \left(3\right) - 1$

Hopefully this helps!