Solve the following equation:

$$
\log \sqrt{7 x+3}+\log \sqrt{4 x+5}=\frac{1}{2}+\log 3
$$
Our equation can also be written as:

$$
\log \sqrt{7 x+3} \cdot \sqrt{4 x+5}=\log 3 \sqrt{10}
$$

or

$$
28 x^{2}+47 x-75=0
$$

which has the positive root $x=1$.

(Neidenbach Emil, Arad.)

Number of solutions: 18.