7.123. $\log _{6} \sqrt[7]{3^{x(15-x)}}+8 \log _{6} 2=8$.
## Solution.

From the condition $\log _{6} 3^{x(15-x) / 7}+\log _{6} 2^{8}=8, \quad \log _{6}\left(3^{x(15-x) / 7} \cdot 2^{8}\right)=8$. Therefore, $3^{x(15-x) / 7} \cdot 2^{8}=6^{8}, 3^{x(15-x) / 7}=3^{8}$. Then $\frac{x(15-x)}{7}=8, x^{2}-15 x+56=0$, from which $x_{1}=7, x_{2}=8$.

Answer: $7 ; 8$.