7.190. $\log _{2} 3+2 \log _{4} x=x^{\frac{\log _{9} 16}{\log _{3} x}}$.
## Solution.

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

From the condition, we have $\log _{2} 3+\log _{2} x=x^{\frac{\log _{3} 4}{\log _{3} x}} \Leftrightarrow \log _{2} 3+\log _{2} x=x^{\log _{x} 4} \Rightarrow$ $\Rightarrow \log _{2} 3+\log _{2} x=4, \log _{2} 3 x=4$, from which $3 x=16, x=\frac{16}{3}$.

Answer: $\frac{16}{3}$.