6.50 If $47^{100}$ is a 168-digit number, then the number of digits in $47^{17}$ is 
(A) 27.
(B) 28.
(C) 29.
(D) 30.
(Xi'an, Shaanxi Province, China Junior High School Mathematics Competition, 1990)
[Solution 1] Given that $47^{100}$ is a 168-digit number, then $\lg 47^{100}=167+a$, where $0 \leqslant a < 1$, 
$$
\therefore \quad 1<a^{\frac{17}{100}} \cdot 10^{\frac{39}{100}}<10$. Then $47^{17}$ is a 29-digit number.
Therefore, the answer is $(C)$.