Write as a logarithm of a single expression.
-$\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k$
A) $\log _ { a } \frac { m } { k ^ { 2 } n }$
B) $\log _ { a } m k^ { 2 } n$
C) $\log _ { a } \frac { 2 m k } { n }$
D) $\log _ { a } \frac { m k ^ { 2 } } { n }$

Question

Quizplus · Accepted Answer

The expression $\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k$ simplifies to $\log _ { a } \frac { m } { n } + \log _ { a } k^2$, which further simplifies to $\log _ { a } \left( \frac { m } { n } \cdot k^2 \right)$, or $\log _ { a } \frac { m k ^ { 2 } } { n }$.

Write as a Logarithm of a Single Expression (log⁡am−log⁡an)+2log⁡ak\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k(loga​m−loga​n)+2loga​k

Write as a Logarithm of a Single Expression $\left( \log _ { a } m - \log _ { a } n \right) + 2 \log _ { a } k$