Q:

How to solve the following logarithm?

How to solve this?? 
The solution is 1001.

A:

Hints: justify using the basic properties of logarithms the following
$$\log(x-1)+\log\sqrt[3]{x^2-1}=4+\frac13\log(x+1)\iff$$
$$\iff\log\left(\frac{(x-1)\sqrt[3]{(x-1)(x+1)}}{\sqrt[3]{x+1}}\right)=4\iff$$
$$\frac43\log(x-1)=4\iff\log(x-1)=3\iff x-1=10^3\;\ldots$$

