Log (x2 - 1) - log (2x + 2) = 0

x=3

Step-by-step explanation:

log (x^2 - 1) - log (2x + 2) = 0

Add log (2x + 2) to each side

log (x^2 - 1) = log (2x + 2)

Since the logs with the same base are equal the x^2 -1 must equal 2x+2

x^2 -1 = 2x+2

Subtract 2x+2 from each side

x^2 -1 -2x-2 = 2x+2 -2x-2

x^2 -2x-3 = 0

Factor

What number multiplies to -3 and adds to -2

-3 *1 =-3

-3+1 =-2

(x-3) (x+1) =0

Using the zero product property

x-3 =0   x+1 =0

x=3  x=-1

Check to see if solutions are valid

x = -1

log ((-1)^2 - 1) - log (2*-1 + 2) = 0

log(0) - log 0 = 0

Log 0 is undefined  x =-1 not a valid solution

x = 3

log ((3)^2 - 1) - log (2*3 + 2) = 0

log(8) - log 8 = 0

valid