Solve the following equation:

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

$$
2^{x}\left(1+2+2^{2}+2^{3}\right)=3^{x}\left(1+3+3^{2}+3^{3}\right)
$$

or

$$
\left(\frac{2}{3}\right)^{x}=\frac{8}{3}
$$

from which

$$
x=\frac{\log 8-\log 3}{\log 2-\log 3}=\frac{3 \log 2-\log 3}{\log 2-\log 3}
$$

(Kornél Miklóssy, Arad.)

Number of solutions: 26.