SOLVE FOR X. logx=log(x+5)-log 2

                                                    log(x) = log(x+5) - log(2)

But the difference of two logs is the log of the quotient of their arguments.

                                                     log(x) = log [ (x+5) / (2) ]

Raise 10 to the power of each side:    x = (x+ 5) / 2

Multiply each side by  2 :                    2x = x + 5

Subtract 'x' from each side :                 x = 5