Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$$\log _ { 5 } \sqrt { 3 x }$$
A) $\log _ { 5 } \sqrt { 3 } + \log _ { 5 } \sqrt { x }$
B) $\frac { 1 } { 2 } \log _ { 5 } 3 x$
C) $\log _ { 5 } 3 + \frac { 1 } { 2 } \log _ { 5 } x$
D) $\frac { 1 } { 2 } \log _ { 5 } 3 + \frac { 1 } { 2 } \log _ { 5 } x$

Question

Quizplus · Accepted Answer

The expression $\log _ { 5 } \sqrt { 3 x }$ can be rewritten using the property that $\log_b \sqrt{a} = \frac{1}{2} \log_b a$, resulting in $\frac { 1 } { 2 } \log _ { 5 } 3 x$. This can be further expanded using the logarithm property $\log_b (mn) = \log_b m + \log_b n$, leading to $\frac { 1 } { 2 } \log _ { 5 } 3 + \frac { 1 } { 2 } \log _ { 5 } x$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much