Rewrite in terms of two or more logarithms using the quotient and product rules for logarithms. Assume all variables
represent positive real numbers.
-$\log _ { w } \left( \frac { 11 x } { 5 } \right)$
A) $\log _ { \mathrm { W } } 11 + \log _ { \mathrm { W } } \mathrm { x } - \log _ { \mathrm { W } } 5$
B) $\log _ { \mathrm { W } } 6 \mathrm { x }$
C) $\log _ { W } 11 + \log _ { W } x + \log _ { W } 5$
D) $\log _ { W } 11 \mathrm { x } - \log _ { \mathrm { W } } 5$

Question

Quizplus · Accepted Answer

The quotient rule for logarithms states that $\log_b \frac{M}{N} = \log_b M - \log_b N$, and the product rule states that $\log_b (MN) = \log_b M + \log_b N$. Applying these rules, $\log_w \frac{11x}{5}$ becomes $\log_w 11 + \log_w x - \log_w 5$.

Rewrite in Terms of Two or More Logarithms Using the Quotient