Answer
$$x=2$$
Work Step by Step
Using the rules of logarithms, we find:
$$\log _{10}\left(x\left(x-1\right)\right)=\log _{10}\left(2\right) \\ x\left(x-1\right)=2 \\ x=2$$
Note, the solution $x=-1$ is ignored because it results in a false statement.
