6.34 If it is known that $\lg 8=0.9031$, and $\lg 9=0.9542$, then the logarithm that cannot be uniquely determined without a logarithm table is
(A) $\lg 17$.
(B) $\lg \frac{5}{4}$.
(C) $\lg 15$.
(D) $\lg 600$.
(E) $\lg 4$.
(2nd American High School Mathematics Examination, 1951)
[Solution] By the properties of logarithms, we have $\lg 8=\lg 2^{3}=3 \lg 2, \lg 9=\lg 3^{2}=2 \lg 3$. Therefore, $\lg 2, \lg 3$ can be determined.

Also, $\lg \frac{5}{4}=\lg \frac{10}{8}=1-\lg 8=1-3 \lg 2$, can be determined;
$\lg 15=\lg 3+\lg 5=\lg 3+1-\lg 2$, can be determined;
$\lg 600=\lg 100+\lg 6=2+\lg 2+\lg 3$, can be determined;
$\lg 4=2 \lg 2, \quad$ can also be determined.

But $\lg 17=\lg (8+9)$, its value cannot be determined according to the given conditions.
Therefore, the answer is $(A)$.