Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
-$\log _ { W } \left( \frac { 9 x } { 5 } \right)$
A) $\log _ { w } 9 + \log _ { W } x - \log _ { w } 5$
B) $\log _ { w } 4 x$
C) $\log _ { W } 9 x - \log _ { W } 5$
D) $\log _ { W } 9 + \log _ { W } x + \log _ { W } 5$

Question

Quizplus · Accepted Answer

By the quotient property of logarithms, we can rewrite $\log_W \left(\frac{9x}{5}\right)$ as $\log_W 9x - \log_W 5$. Then, using the product property of logarithms, we can further expand $\log_W 9x$ as $\log_W 9 + \log_W x$. Putting these together, we get $\log_W 9 + \log_W x - \log_W 5$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much