Question

log (x-4) + log (x+5)=1

Answer 1

log((x-4)(x+5)) = log e

(x-4)(x-5) = e

Answer 2

But what does x equal?

Answer 3

log (x-4) + log (x+5)=1

log[ (x-4)(x+5) ]=1

(x-4)(x+5) = 10^1

(x-4)(x+5) = 10

x^2+x-20 = 10

x^2+x-20 - 10 =0

x^2+x-30 =0

(x-5)(x+6) = 0

x-5=0 or x+6=0

x=5 or x=-6

Throw out the possible solution x = -6 since it's NOT in the domain.


So the only answer is x = 5