Since log a - log b = log a/b, you can get rid of the logs as this:
(3+x)/(x+5) = 5 =>
3+x = 5(x+5) => 5x + 25 - x - 3 = 0 => 4x = -22 => x = -5.5
log(3 + x) - log (x + 5) = log 5, By the Laws of Logarithms:-
log [(3 + x) / (x + 5)] = log 5
(3 + x)/(x + 5) = 5
3 + x = 5x + 25
4x = -22
x -== -5.5
Since there is no log of a negative number there is no solution
