How do you solve log_3 (5x+5) - log_3 (x^2 - 1) = 0?

1 Answer
May 11, 2015

The answer is x=6

I recall the rule:
log(a)-log(b)=log(a/b)
and log(a)=0 <=> a=1

so log_3((5x+5)/(x^2-1))=0 <=>

<=> (5x+5)/(x^2-1)=1 <=> 5x+5=x^2-1

So we gotta solve x^2-5x-6=0

(5+-sqrt(25+24))/2 = (5+-7)/2 => x=6 or x=-1

6 is an acceptable solution:

5*6+5=35>0 and 36-1=35>0

-1 is not an acceptable answer:
-5+5=0 and log(0) is not defined, so that solution is an extraneous solution.