1B. In the set of real numbers, solve the equation

$$
\log _{x+1}\left(x^{3}-9 x+8\right) \cdot \log _{x-1}(x+1)=3
$$
Solution. The given equation is equivalent to the equation $x^{3}-9 x+8=(x-1)^{3}$.

By simplification, we get $x^{2}-4 x+3=0$, whose solutions are $x_{1}=1, x_{2}=3$.

The solution $x_{1}=1$ is discarded due to the definition of the logarithmic function. It is easily verified that $x=3$ is a solution to the original equation.