7.185. $6-\left(1+4 \cdot 9^{4-2 \log _{\sqrt{3}} 3}\right) \log _{7} x=\log _{x} 7$.
## Solution.

Domain of definition: $0<x \neq 1$.

Switch to base 7. We have $6-\left(1+4 \cdot 9^{0}\right) \log _{7} x=\frac{1}{\log _{7} x} \Leftrightarrow$ $\Leftrightarrow 5 \log _{7}^{2} x-6 \log _{7} x+1=0$. Solving this equation as a quadratic in terms of $\log _{7} x$, we get $\left(\log _{7} x\right)_{1}=\frac{1}{5}$ or $\left(\log _{7} x\right)_{2}=1$, from which $x_{1}=\sqrt[5]{7}, x_{2}=7$.

Answer: $\sqrt[5]{7} ; 7$.