Question

solve the equation log(x-5) + log(x+2) = 1 algebraically . find any extraneous solution. if there is no extaneouse answer why?

Answer 1

log(x-5) + log(x+2) = 1
log[(x-5)(x+2)] = 1
(x-5)(x+2) = 10
x^2 - 3x - 20 = 0
x = 6.216990566028302 or -3.2169905660283016 (N.A. since x > 0)
x ≈ 6.217