8・3 If $4^{x}-4^{x-1}=24$, then $(2 x)^{x}$ equals
(A) $5 \sqrt{5}$.
(B) $\sqrt{5}$.
(C) $25 \sqrt{5}$.
(D) 125 .
(E) 25 .
(9th American High School Mathematics Examination, 1958)
[Solution] From $4^{x}-4^{x-1}=24$, we get $\quad 4^{x-1}(4-1)=24$, which means $4^{x-1}=8$, which can be transformed into $\quad 2^{2(x-1)}=2^{3}$, then $2(x-1)=3$, yielding $x=\frac{5}{2}$.
$$
\therefore \quad(2 x)^{x}=\left(2 \cdot \frac{5}{2}\right)^{\frac{5}{2}}=25 \sqrt{5} \text {. }
$$

Therefore, the answer is $(C)$.