By what power should $\frac{32}{243}$ be raised to obtain $\frac{27}{8}$?
Let $x$ be the sought number, then

$$
\left(\frac{32}{243}\right)^{x}=\frac{27}{8}
$$

or

$$
\begin{aligned}
\left(\frac{2}{3}\right)^{5 x} & =\left(\frac{3}{2}\right)^{3} \\
\left(\frac{2}{3}\right)^{5 x} & =\left(\frac{2}{3}\right)^{-3}
\end{aligned}
$$

thus

$$
\begin{aligned}
& 5 x=-3 \\
& x=-\frac{3}{5}
\end{aligned}
$$

(Jenö Bóhm, Pécs.)

The problem was also solved by: Bauer E., Breuer P., Dénes M., Engler J., Erdős V., Fried E., Gianone O., Grün E., Grünvald Gy., Koffler B., Köhler I., Mattyasovszky L., Neumann L., Rosenberg E., Sichermann F., Spitzer L., Szilárd V., Vilcsek A., Viola R., Weinberger Gy., the VII. district physics and chemistry circle.