Solve the following equation:

$$
2^{x+3}+4^{x+1}=320 .
$$
Our equation can also be written as:

$$
8 \cdot 2^{x} + 4 \cdot 2^{2 x} = 320
$$

from which

$$
2^{x} = -1 \pm 9
$$

and thus the usable value of $x$ is 3.

(István Hegedűs, Hódmezővásárhely.)

Number of solutions: 52.