Answer
x=5
Work Step by Step
Using the rules of logarithms to solve the equation, we find:
$$\log _{10}\left(5x\left(x-1\right)\right)=2 \\ 5x\left(x-1\right)=100 \\ x=5,\:x=-4$$
Checking for extraneous solutions, we see that only $x=5$ is valid.
