Question

Write each expression as a single logarithm.

$2{\log }_{3}u-{\log }_{3}v$

Short answer

The result is${\log }_3\left(\frac{u^2}{v}\right)$.

Step-by-step solution

Step 1. Given information.

Consider the given information.

$2{\log }_{3}u-{\log }_{3}v$

Step 2. Calculation.

Apply the property ${\log }_a\left(\frac{M}{N}\right)={\log }_{a}M-{\log }_{a}N$.

role="math" localid="1646759695907" $\begin{array}{rcl}2{\log }_{3}u-{\log }_{3}v& =& {\log }_3{u}^2-{\log }_{3}v\\ & =& {\log }_3\left(\frac{u^2}{v}\right)\end{array}$