Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 7 } \frac { \sqrt [ 5 ] { x } \sqrt [ 8 ] { y } } { z ^ { 2 } }$
A) $\frac { 5 } { 7 } \log _ { 7 } x + \frac { 8 } { 7 } \log _ { 7 } y - \frac { 2 } { 7 } \log _ { 7 } z$
B) $\frac { 1 } { 5 } \log _ { 7 } x + \frac { 1 } { 8 } \log _ { 7 } y - 2 \log _ { 7 } z$
C) $\frac { 1 } { 5 } \log _ { 7 } x * \frac { 1 } { 8 } \log _ { 7 } y \div 2 \log _ { 7 } z$
D) $5 \log _ { 7 } x + 8 \log _ { 7 } y - 2 \log _ { 7 } z$

Question

Use properties of logarithms to expand the logarithmic expression as much as possible.
-$\log _ { 7 } \frac { \sqrt [ 5 ] { x } \sqrt [ 8 ] { y } } { z ^ { 2 } }$
A) $\frac { 5 } { 7 } \log _ { 7 } x + \frac { 8 } { 7 } \log _ { 7 } y - \frac { 2 } { 7 } \log _ { 7 } z$
B) $\frac { 1 } { 5 } \log _ { 7 } x + \frac { 1 } { 8 } \log _ { 7 } y - 2 \log _ { 7 } z$
C) $\frac { 1 } { 5 } \log _ { 7 } x *  \frac { 1 } { 8 } \log _ { 7 } y \div 2 \log _ { 7 } z$
D) $5 \log _ { 7 } x + 8 \log _ { 7 } y - 2 \log _ { 7 } z$

Quizplus · Accepted Answer

The expression can be expanded using the properties of logarithms: the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$, the product rule $\log_b (MN) = \log_b M + \log_b N$, and the power rule $\log_b M^k = k \log_b M$. Applying these rules, we get $\frac{1}{5} \log_7 x + \frac{1}{8} \log_7 y - 2 \log_7 z$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much