Answer
$x=-1$ and $x=4$
Work Step by Step
$\log_{4}(x^{2}-3x)=1$
Rewrite in exponential form:
$4^{1}=x^{2}-3x$
$x^{2}-3x=4$
Take the $4$ to the left side of the equation:
$x^{2}-3x-4=0$
Solve this equation by factoring:
$(x+1)(x-4)=0$
Set each factor equal to $0$ and solve each individual equation for $x$:
$x+1=0$
$x=-1$
$x-4=0$
$x=4$
The initial equation is not undefined for either of the solutions found. Our answer is $x=-1$ and $x=4$