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

Question

Quizplus · Accepted Answer

The expression can be expanded using the property of logarithms that $\log_b(mn) = \log_b m + \log_b n$. Since $25 = 5^2$, $\log_5(25x) = \log_5(5^2) + \log_5(x) = 2 + \log_5(x)$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much