Log (3+x) - log (x+5) = log 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

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