Question

solve for x
log x=log(x-2)+log2

Answer 1

4

Answer 2

Notice first that log(x-2) + log 2 = log (2(x-2)) = log(2x - 4)

Hence the LHS = RHS if and only if x = 2x - 4, or 4 = x.

And indeed when x = 4,
log x = log 4
= 2.log 2
= log (2) + log (2)
= log(x-2) + log 2.