Answer
False
Work Step by Step
We are given the following equation:
$\log_4{7}-\log_4{3}=\log_4{4}$
Recall the quotient property of logarithms (pg. 462):
$\log_b{\frac{m}{n}}=\log_b{m}-\log_b{n}$
We apply this property to the left side of our equation:
$\log_4{7}-\log_4{3}\stackrel{?}{=}\log_4{4}$
$\log_4{\frac{7}{3}}\stackrel{?}{=}\log_4{4}$
Note that $\log_a{m} = \log_a{n} \implies m=n$
Since $\frac{7}{3} \approx 2.33$, then $\frac{7}{3} \ne 4$ and
$\log_4{\frac{7}{3} }\ne\log_4{4}$
Thus we see that the statement is false.
