Answer
$x=5$
Work Step by Step
$\log x+\log(x-3)=1$
Combine the logarithms on the left side of the equation as a product:
$\log x(x-3)=1$
$\log(x^{2}-3x)=1$
Write this equation in exponential form:
$x^{2}-3x=10^{1}$
$x^{2}-3x=10$
Take the $10$ to the left side of the equation:
$x^{2}-3x-10=0$
Solve by factoring:
$(x+2)(x-5)=0$
We get two solutions:
$x=-2$ and $x=5$
The initial equation is undefined at $x=-2$, so we can discard that solution.
Our final answer is $x=5$.
