Question 138622
log2(x-1) = 1 + log2 (x-5)
log2(x-1) - log2 (x-5)= 1
log2((x-1)/(x-5))=1 (because log(a)-log(b)=log(a/b))
x-1/x-5=2
x-1=2x-10
-x+9=0
x=9

checking:

log2(8)=1+log2(4)
3=1+2

Answer: x=9