#### Answer

$\log_5{125}=3$

#### Work Step by Step

Let
$x=\log_5{125}.$
RECALL:
$\log_{a}{y} = b \longleftrightarrow a^b = y.$
Use the definition above to convert the equation to an exponential equation and have
$5^x=125.$
Write each side in base 5 to have
$5^x=5^3.$
The bases are the same, so the exponents must be equal. Thus,
$x=3.$
Therefore $\log_5{125}=3$.