Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 4 } \frac { x ^ { 3 } } { y ^ { 6 } }$
A) $3 \log _ { 4 } x - 6 \log _ { 4 } y$
B) $\frac { 1 } { 2 } \log _ { 4 } \frac { x } { y }$
C) $3 \log _ { 4 } x + 6 \log _ { 4 } y$
D) $6 \log _ { 4 } y - 3 \log _ { 4 } x$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the expression $\log _ { 4 } \frac { x ^ { 3 } } { y ^ { 6 } }$ can be expanded as $3 \log _ { 4 } x - 6 \log _ { 4 } y$. This uses the quotient rule $\log_b \frac{M}{N} = \log_b M - \log_b N$ and the power rule $\log_b M^k = k \log_b M$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much