$8 \cdot 22$ The product of all real roots of the equation $x^{\lg x}=10$ is
(A) 1 .
(B) -1 .
(C) 10 .
(D) $10^{-1}$
(E) None of the above.
(35th American High School Mathematics Examination, 1984)
［Sol］Take the logarithm with base 10 on both sides of the given equation

i.e. $\square$
$$
(\lg x)(\lg x)=1,
$$

then
we get
$$
\begin{array}{c}
(\lg x)^{2}=1, \\
\lg x= \pm 1, \\
x=10 \text { or } 10^{-1} .
\end{array}
$$

It can be verified that they are all roots of the original equation, so their product is 1. Therefore, the answer is $(A)$.