Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
-$$\log _ { 2 } \left( \frac { 1 } { 32 } p ^ { 3 } q \right)$$
A) $- 5 + 3 \log _ { 2 } p + \log _ { 2 } q$
B) $\frac { 1 } { 5 } + 3 \log _ { 2 } p + \log _ { 2 } q$
C) $- 15 \log _ { 2 } p + \log _ { 2 } q$
D) $\frac { 3 } { 5 } \log _ { 2 } p + \log _ { 2 } q$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the given expression can be rewritten as a sum or difference of logarithms. The expression inside the logarithm can be separated into its components: $\log_2\left(\frac{1}{32}\right) + \log_2(p^3) + \log_2(q)$. Since $32 = 2^5$, $\log_2\left(\frac{1}{32}\right) = \log_2(2^{-5}) = -5$. Also, $\log_2(p^3) = 3\log_2(p)$ and $\log_2(q)$ remains as it is. Therefore, the expression simplifies to $-5 + 3\log_2(p) + \log_2(q)$.

Write the Logarithm as a Sum or Difference of Logarithms log⁡2(132p3q)\log _ { 2 } \left( \frac { 1 } { 32 } p ^ { 3 } q \right)log2​(321​p3q)

Write the Logarithm as a Sum or Difference of Logarithms $\log _ { 2 } \left( \frac { 1 } { 32 } p ^ { 3 } q \right)$