Answer
$x=3$
Work Step by Step
$\log_{4}(x+2)+\log_{4}3=\log_{4}5+\log_{4}(2x-3)$
Combine the logarithms on the left and right side of the equation as products:
$\log_{4}(3x+6)=\log_{4}(10x-15)$
Since $\log$ is one to one, the equation becomes:
$3x+6=10x-15$
Solve for $x$:
$3x-10x=-15-6$
$-7x=-21$
$x=3$