Answer:
x=3
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