## College Algebra (11th Edition)

$\log_a\dfrac{xy}{m}$
$\bf{\text{Solution Outline:}}$ Use the Laws of Logarithms to write the given expression, $\log_ax+\log_ay-\log_am ,$ as a single logarithm. $\bf{\text{Solution Details:}}$ Using the Product Rule of Logarithms, which is given by $\log_b (xy)=\log_bx+\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_a(xy)-\log_am .\end{array} Using the Quotient Rule of Logarithms, which is given by $\log_b \dfrac{x}{y}=\log_bx-\log_by,$ the expression above is equivalent \begin{array}{l}\require{cancel} \log_a\dfrac{xy}{m} .\end{array}