Answer
$2-\log_5{x}$
Work Step by Step
Recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
Applying the quotient proeprty to the given expression gives:
$\log_5{\frac{25}{x}}=\log_5{25}-\log_5{x}$
Next, recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
We use this property to simplify further:
\begin{align*}
\log_5{25}-\log_5{x}&=\log_5{5^2}-\log_5{x}\\
&=2\log_5{5}-\log_5{x}\\
&=2\times1-\log_5{x}\\
&=2-\log_5{x}
\end{align*}
Here we used the fact that $\log_5{5}=1$ (because $5^1=5$).
