How do you solve the equation log_3(x+5)-log_3(x-7)=2?

1 Answer
Feb 17, 2015

You can use the following facts:

log_aM-log_aN=log(M/N) and:

log_ab=x => a^x=b

So you get:

log_3(x+5)-log_3(x-7)=2
log_3((x+5)/(x-7))=2
(x+5)/(x-7)=3^2
x+5=9(x-7)
x-9x=-63-5
-8x=-68
x=68/8=17/2