Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
-$2 \log _ { b } m - \log _ { b } n$
A) $\log _ { \mathrm { b } } \left( \frac { \mathrm { m } ^ { 2 } } { \mathrm { n } } \right)$
B) $\log _ { \mathrm { b } } \mathrm { m } ^ { 2 } \div \log _ { \mathrm { b } } \mathrm { n }$
C) $\log _ { b } \left( \frac { 2 m } { n } \right)$
D) $\log _ { \mathrm { b } } \left( \mathrm { m } ^ { 2 } - \mathrm { n } \right)$

Question

Quizplus · Accepted Answer

The expression can be condensed using the properties of logarithms: $2 \log _ { b } m$ becomes $\log _ { b } m^2$ (using the power rule), and subtracting $\log _ { b } n$ can be represented as division inside a single logarithm, resulting in $\log _ { b } \left( \frac { m ^ { 2 } } { n } \right)$.

Use Properties of Logarithms to Condense the Logarithmic Expression 2log⁡bm−log⁡bn2 \log _ { b } m - \log _ { b } n2logb​m−logb​n

Use Properties of Logarithms to Condense the Logarithmic Expression $2 \log _ { b } m - \log _ { b } n$