Solve for real x:log(5) (x+4) = log(5) (5x+5)
log(5) (x+4) = log(5) (5x+5).
We are required to solve for x:
Since both sides have the same base of the logarithms, we take antilog with respect to the base 5.
x+4 = 5x+5.
We isolate x to left and numbers to right.
x-5x = 5-4
-4x = 1
x = 1/-4.
x = 1/4.
So x= -1/4.
Before solving the equation, we'll impose conditions of existence of the logarithms.
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:
We'll move all terms to one side:
-4x - 1=0
We'll add 1 both sides:
-4x = 1
x = -1/4
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).