17. Suppose $x=3^{\sqrt{2+\log _{3} x}}$ is an integer. Determine the value of $x$.
17. Answer: 9
Taking logarithm, we get $\log _{3} x=\sqrt{2+\log _{3} x}$ Let $y=\log _{3} x$. The only possible solution for $y=\sqrt{2+y}$ is 2 . Therefore $x=3^{2}=9$.