7.070. $4^{\log _{9} x^{2}}+\log _{\sqrt{3}} 3=0.2\left(4^{2+\log _{9} x}-4^{\log _{9} x}\right)$.
## Solution.

Domain of definition: $x>0$.

Rewrite the equation as

$4^{2 \log _{9} x}+2 \log _{3} 3=0.2\left(16 \cdot 4^{\log _{9} x}-4^{\log _{9} x}\right) \quad 4^{2 \log _{9} x}-3 \cdot 4^{\log _{9} x}+2=0$.

Solving this equation as a quadratic equation in terms of $4^{\log _{9} x}$, we find $\left(4^{\log _{9} x}\right)=1$, from which $\left(\log _{9} x\right)_{1}=0, x_{1}=1$, or $\left(4^{\log _{9} x}\right)_{2}=2$, from which $\left(\log _{9} x\right)_{2}=\frac{1}{2}, x_{2}=3$.

Answer: $1 ; 3$.