7.084. $\frac{2^{x}+10}{4}=\frac{9}{2^{x-2}}$.

7.084. $\frac{2^{x}+10}{4}=\frac{9}{2^{x-2}}$.
## Solution.

From the condition

$$
\frac{2^{x}+10}{4}=\frac{9}{2^{x} \cdot 2^{-2}}, \frac{2^{x}+10}{4}=\frac{36}{2^{x}}, 2^{2 x}+10 \cdot 2^{x}-144=0 .
$$

Solving this equation as a quadratic in terms of $2^{x}$, we find $2^{x}=-18, \varnothing$, or $2^{x}=8$, from which $x=3$.

Answer: 3.