Question

solve
log(2+x)-log(x-3)=log2
Reiny
log(2+x)-log(x-3)=log2
log( (2+x)/(x-3) ) = log2
"unlog" it
(2+x)/(x-3) = 2
2x - 6 = 2+x
x = 8

check it with your calculator