Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$
A) $\frac { 5 } { 9 } \left( \log _ { 2 } p - \log _ { 2 } q \right)$
B) $\frac { 5 } { 9 } \left( \log _ { 2 } p + \log _ { 2 } q \right)$
C) $- 4 \left( \log _ { 2 } p - \log _ { 2 } q \right)$
D) $5 \log _ { 2 } p - 9 \log _ { 2 } q$

Question

Quizplus · Accepted Answer

Using the logarithm properties, $\log _ { b } \frac { x } { y } = \log _ { b } x - \log _ { b } y$ and $\log _ { b } x ^ { n } = n \log _ { b } x$, the expression simplifies to $5 \log _ { 2 } p - 9 \log _ { 2 } q$.

Write the Logarithm as a Sum or Difference of Logarithms log⁡2p5q9\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }log2​q9p5​

Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 2 } \frac { p ^ { 5 } } { q ^ { 9 } }$