Solve the following equation:

$$
3125^{\frac{x+1}{x+2}} \cdot 15625^{-\frac{x+2}{x+3}}=0.2
$$
Since

$$
3125=5^{5}, 15625=5^{6} \text { and } 0.2=\frac{1}{5}=5^{-1}
$$

our equation can also be written as:

$$
5^{5 \cdot \frac{x+1}{x+2}-6 \cdot \frac{x+2}{x+3}}=5^{-1}
$$

thus

$$
5 \cdot \frac{x+1}{x+2}-6 \cdot \frac{x+2}{x+3}=-1
$$

or

$$
5(x+1)(x+3)-6(x+2)^{2}=-(x+2)(x+3) .
$$

By performing the multiplication, we obtain that

$$
x=3
$$

(Jánosy Gyula, Budapest.)

The problem was also solved by: Fekete M., Harsányi Z., Heimlich P., Kiss J., Paunz A., Pichler S., Schuster Gy., Szécsi J., Tóth B.