log (2x) - log (x+4) = log 5

We'll impose the constraints of existence of
logarithms:

2x>0

x>0

x+4>0

x>-4

The
common interval of values that satisfies both constraints is (-0 ,
+inf.).

Now, we'll solve the equation. First, we'll add log
(x+4) both sides:

log (2x) - log (x+4) + log (x+4) = log 5
+ log (x+4)

log (2x) = log 5 + log
(x+4)

Now, we'll use the product property of the
logarithms:

log (2x) = log
5*(x+4)

Because the logarithms have matching bases, we'll
use the one to one property:

2x = 5x +
20

We'll subtract 5x both
sides:

2x-5x = 20

-3x =
20

We'll divide by -3:

x =
-20/3 < 0

Since the solution is negative, is not
admissible, so the equation has no solutions!