Answer
$x=4$
Work Step by Step
$\log_{2}x+\log_{2}(x-3)=2$
Combine the logarithms on the left side of the equation as a product:
$\log_{2}x(x-3)=2$
$\log_{2}(x^{2}-3x)=2$
Write this equation in exponential form:
$x^{2}-3x=2^{2}$
$x^{2}-3x=4$
Take the $4$ to the left side of the equation:
$x^{2}-3x-4=0$
Solve by factoring:
$(x+1)(x-4)=0$
We get two solutions:
$x=-1$ and $x=4$
The initial equation is undefined in $x=-1$, so we discard that solution.
Our final answer is $x=4$.
