A1. What is the solution to the equation $\sqrt[5]{9^{x-3}}-\frac{1}{\sqrt{3}}=0$ ?
(A) $x=-\frac{7}{4}$
(B) $x=-\frac{4}{7}$
(C) $x=\frac{4}{7}$
(D) $x=\frac{7}{4}$
(E) $x=-\frac{9}{4}$
A1. We transform the equation into the form $9^{\frac{x-3}{5}}=\frac{1}{\sqrt{3}}$ and rewrite it as $3^{\frac{2 x-6}{5}}=3^{-\frac{1}{2}}$. When we solve this exponential equation, we get the solution $\frac{7}{4}$. The correct answer is $D$.