$8 \cdot 26$ The set of values of $x$ that satisfy the equation $x^{\lg x}=\frac{x^{3}}{100}$ is composed of the elements
(A) only $\frac{1}{10}$.
(B) only 10.
(C) only 100.
(D) only 10 or 100.
(E) more than two real numbers.
（13th American High School Mathematics Examination, 1962）
[Solution] Taking the logarithm (common logarithm) of both sides of the equation, we have
that is $\square$
$$
\lg x \cdot \lg x=3 \lg x-\lg 100,
$$
$\lg ^{2} x-3 \lg x+2=0$, yielding $\lg x=1$ or 2.
Thus, $x=10$ or 100.
Therefore, the answer is $(D)$.