Answer
$x=5$
Work Step by Step
$\log x+\log(x-1)=\log(4x)$
Combine the sum of logarithms present on the left side of the equation as a product:
$\log x(x-1)=\log(4x)$
Since $\log$ is one to one, this equation becomes:
$x(x-1)=4x$
Solve for $x$:
$x^{2}-x-4x=0$
$x^{2}-5x=0$
$x(x-5)=0$
The solutions are:
$x=0$ and $x=5$
Verify the solutions:
$x=5$ True
$x=0$ False
The final answer:
$x=5$
