Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { 5 } ( 25 x )$
A) $2 + \log _ { 5 } x$
B) $2 \mathrm { x }$
C) $10 + \log _ { 5 } x$
D) $2 \log _ { 5 } x$

Question

Quizplus · Accepted Answer

The expression $\log _ { 5 } ( 25 x )$ can be expanded using the properties of logarithms. Specifically, $\log _ { 5 } ( 25 x ) = \log _ { 5 } (5^2 \cdot x) = \log _ { 5 } (5^2) + \log _ { 5 } x = 2 + \log _ { 5 } x$, because $\log _ { b } (a \cdot c) = \log _ { b } a + \log _ { b } c$ and $\log _ { b } (b^k) = k$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much