Log5 (x+6) - log5 (x+2) = log5x

X = 2

Use the log rules to condense the left side.

log5 ((x+6) / (x+2)) = log5x

log 5 will cancel on both sides.

(x+6) / (x+2) = x

Solving you get x=2 and x = - 3. The domain of log is x >0 so the - 3 is an extraneous solution.