8.17 Given $\log _{x} a=a$ (where $a$ is a positive integer greater than 1), then the value of $x$ is
(A) $10^{a \lg a}$.
(B) $10 a^{\frac{\lg a}{2}}$.
(C) $10^{\frac{\lg a}{a}}$.
(D) $10^{a \lg \frac{1}{a}}$.
(China Junior High School Mathematics League, 1986)
[Solution] $\because \quad \log _{x} a=a$, then $x^{a}=a$, thus $\lg x=\frac{\lg a}{a}, \therefore \quad x=10^{\frac{\lg a}{a}}$. Therefore, the answer is $(C)$.