Write the logarithmic expression as a single logarithm with coefficient 1, and simplify as much as
possible.
-$$3 \log _ { 5 } m - 8 \log _ { 5 } n$$
A) $\log _ { 5 } \left( m ^ { 3 } - n ^ { 8 } \right)$
B) $\log _ { 5 } \frac { m ^ { 3 } } { n ^ { 8 } }$
C) $\frac { 3 } { 8 } \log _ { 5 } \frac { m } { n }$
D) $\log _ { 5 } ( 3 m - 8 n )$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to write the expression as a single logarithm: $\log_a(x^m) = m \log_a(x)$ and $\log_a(x) - \log_a(y) = \log_a(\frac{x}{y})$. Applying these, we get $\log_5\left(\frac{m^3}{n^8}\right)$.

Write the Logarithmic Expression as a Single Logarithm with Coefficient 3log⁡5m−8log⁡5n3 \log _ { 5 } m - 8 \log _ { 5 } n3log5​m−8log5​n

Write the Logarithmic Expression as a Single Logarithm with Coefficient $3 \log _ { 5 } m - 8 \log _ { 5 } n$