Answer
$\log_a\dfrac{m}{nt}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Laws of Logarithms to write the given expression, $
\log_am-\log_an-\log_at
,$ as a single logarithm.
$\bf{\text{Solution Details:}}$
Grouping the last two terms, the expression above is equivalent to
\begin{array}{l}\require{cancel}
\log_am-(\log_an+\log_at)
.\end{array}
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_am-(\log_a(nt))
.\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{m}{nt}
.\end{array}
