Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers.
-$3 \log _ { m } y - 7 \log _ { m } x ^ { 2 }$
A) $\log _ { m } \left( \frac { 3 y } { 7 x ^ { 2 } } \right)$
B) $\log _ { m } \left( \frac { \mathrm { y } ^ { 3 } } { \mathrm { x } ^ { 14 } } \right)$
C) $\log _ { m } \left( \frac { y ^ { 3 } } { x ^ { 9 } } \right)$
D) $\frac { \log _ { m } \mathrm { y } ^ { 3 } } { \log _ { \mathrm { m } } 14 }$

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to write $3 \log _ { m } y$ as $\log _ { m } y^3$ and $7 \log _ { m } x^2$ as $\log _ { m } x^{14}$. Subtracting these gives $\log _ { m } \left( \frac { y^3 } { x^{14} } \right)$, which matches choice B.

Write the Expression as a Single Logarithm with Coefficient 1 3log⁡my−7log⁡mx23 \log _ { m } y - 7 \log _ { m } x ^ { 2 }3logm​y−7logm​x2

Write the Expression as a Single Logarithm with Coefficient 1 $3 \log _ { m } y - 7 \log _ { m } x ^ { 2 }$