Answer
$log_a(\frac{1}{p^2})$
Work Step by Step
$\frac{1}{2}log_a(p^3q^4)-\frac{2}{3}log_a(p^4q^3)=log_a(p^{3/2}q^2)-log_a(p^{8/3}q^2)=log_a(\frac{p^{3/2}q^2}{p^{8/3}q^2})=log_a(\frac{1}{p^2})$
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