Write as a logarithm of a single expression.
-$3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r$
A) $\log _5 \frac { 27 \sqrt [ 7 ] { r - 7 } } { \sqrt { r } }$
B) $\log _5 \left( \frac { 3 } { 14 } \sqrt { \frac { r - 7 } { r } } \right)$
C) $\log _ { 5 } \sqrt { \frac { 3 r - 21 } { 14 r } }$
D) $\log _5 \frac { 27 r - 7 } { 14 r }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression can be simplified as follows: $3 \log _ { 5 } 3$ becomes $\log_5 3^3 = \log_5 27$, $\frac { 1 } { 7 } \log _ { 5 } ( r - 7 )$ becomes $\log_5 (r-7)^{1/7}$, and $- \frac { 1 } { 2 } \log _ { 5 } r$ becomes $\log_5 r^{-1/2} = \log_5 \frac{1}{\sqrt{r}}$. Combining these using the product and quotient rules for logarithms results in $\log _5 \frac { 27 \sqrt [ 7 ] { r - 7 } } { \sqrt { r } }$.

Write as a Logarithm of a Single Expression 3log⁡53+17log⁡5(r−7)−12log⁡5r3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r3log5​3+71​log5​(r−7)−21​log5​r

Write as a Logarithm of a Single Expression $3 \log _ { 5 } 3 + \frac { 1 } { 7 } \log _ { 5 } ( r - 7 ) - \frac { 1 } { 2 } \log _ { 5 } r$