Rewrite as a single logarithm.
-$2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k$
A) $\log _ { b } \frac { m ^ { 2 } k ^ { 4 } } { j 1 / 6 n ^ { 4 / 5 } }$
B) $\log _ { b } \frac { m ^ { 2 } n ^ { 4 / 5 } } { j 1 / 6 k ^ { 4 } }$
C) $\log _ { b } \left( 2 m - \frac { 4 } { 5 } n + \frac { 1 } { 6 } j - 4 k \right)$
D) $\log _ { b } \frac { m ^ { 2 } j ^ { 1 / 6 } } { n ^ { 4 / 5 } k ^ { 4 } }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow for the combination of multiple logarithmic expressions into a single one. Specifically, $a\log_b(x) = \log_b(x^a)$ and $\log_b(x) - \log_b(y) = \log_b(\frac{x}{y})$. Applying these rules, the given expression simplifies to $\log_b\left(\frac{m^2 \cdot j^{1/6}}{n^{4/5} \cdot k^4}\right)$.

Rewrite as a Single Logarithm 2log⁡bm−45log⁡bn+16log⁡bj−4log⁡bk2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k2logb​m−54​logb​n+61​logb​j−4logb​k

Rewrite as a Single Logarithm $2 \log _ { b } m - \frac { 4 } { 5 } \log _ { b } n + \frac { 1 } { 6 } \log _ { b } j - 4 \log _ { b } k$