7.245. $\log _{1+x}\left(2 x^{3}+2 x^{2}-3 x+1\right)=3$.
Solution.

Domain of definition: $\left\{\begin{array}{l}2 x^{3}+2 x^{2}-3 x+1>0, \\ -1<x \neq 0 .\end{array}\right.$

We have

$$
\begin{aligned}
& 2 x^{3}+2 x^{2}-3 x+1=(1+x)^{3} \Leftrightarrow 2 x^{3}+2 x^{2}-3 x+1=1+3 x+3 x^{2}+x^{3} \Leftrightarrow \\
& \Leftrightarrow x^{3}-x^{2}-6 x=0 \Leftrightarrow x\left(x^{2}-x-6\right)=0
\end{aligned}
$$

from which $x_{1}=0, x_{2}=-2, x_{3}=3 ; x_{1}=0, x_{2}=-2$ do not satisfy the domain of definition.

Answer: 3.