Use the properties of logarithms to simplify the logarithmic expression below. $\log _ { 5 } \sqrt { 175 }$
A) $2 \log _ { 5 } 7$
B) $1 + \frac { 1 } { 2 } \log _ { 5 } 7$
C) $2 + \frac { 1 } { 2 } \log _ { 5 } 7$
D) $2 + \log _ { 5 } 7$
E) $1 + \log _ { 5 } 7$

Question

Quizplus · Accepted Answer

First, simplify $\sqrt{175}$ as $5\sqrt{7}$. Then, use the properties of logarithms: $\log_5(5\sqrt{7}) = \log_5(5) + \log_5(\sqrt{7})$. Since $\log_5(5) = 1$ and $\log_5(\sqrt{7}) = \frac{1}{2}\log_5(7)$, the expression simplifies to $1 + \frac{1}{2}\log_5(7)$.

Use the Properties of Logarithms to Simplify the Logarithmic Expression log⁡5175\log _ { 5 } \sqrt { 175 }log5​175​

Use the Properties of Logarithms to Simplify the Logarithmic Expression $\log _ { 5 } \sqrt { 175 }$