Solve for real x:log(5) (x+4) = log(5) (5x+5)

Before solving the equation, we'll impose conditions of
existence of the
logarithms.

x+4>0

x>-4

and

5(x+1)>0

x>-1

The
range of values admissible, for the equation to exist: (-1,
+inf).

We notice that the logarithms have matching bases,
so we can apply the one to one
property:

x+4=5x+5

We'll move
all terms to one
side:

x-5x+4-5=0

-4x -
1=0

We'll add 1 both
sides:

-4x = 1

x =
-1/4

x=-0.25

After finding the
value for x, we'll have to check if it is a solution for the equation, so, we'll have to
verify if it is belonging to the range of values (-1, +inf). We notice that -0.25 is
belonging to the interval (-1,
+inf).

x=-0.25