7.61 $\log _{2} 3+2 \log _{4} x=x^{\frac{\log _{9} 16}{\log _{3} x}}$.

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7.61 $\log _{2} 3+2 \log _{4} x=x^{\frac{\log _{9} 16}{\log _{3} x}}$.
7.61 Here $x>0$. Simplify the right side of the equation

$$
x^{\frac{\log _{2} 16}{\log _{3} x}}=\left(x^{\log _{x} 3}\right)^{\log _{3} 4}=3^{\log _{3} 4}=4
$$

Now write the equation in the form

$\log _{4} 9+\log _{4} x^{2}=4 \log _{4} 4$, or $\log _{4}\left(9 x^{2}\right)=\log _{4} 4^{4}$,

i.e., $9 x^{2}=4^{4}$, from which $x_{1,2}= \pm \frac{16}{3}$. The condition $x>0$

is satisfied only by the root $x=\frac{16}{3}$.

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