7.183. $5^{-2 \log _{0.04}\left(3-4 x^{2}\right)}+1.5 \log _{1 / 8} 4^{x}=0$.
## Solution.

Domain of definition: $3-4 x^{2}>0 \Leftrightarrow-\frac{\sqrt{3}}{2}<x<\frac{\sqrt{3}}{2}$.

From the condition

$$
5^{\log _{5}\left(3-4 x^{2}\right)}+1.5 x \log _{2^{-3}} 2^{2}=0 \Leftrightarrow 3-4 x^{2}-x=0 \Leftrightarrow 4 x^{2}+x-3=0
$$

from which $x_{1}=-1, x_{2}=\frac{3}{4} ; x_{1}=-1$ does not satisfy the domain of definition.

Answer: $\frac{3}{4}$.