How do you solve log_5 (x+3)= 3 + log_5 (x-3) ?

1 Answer
Apr 10, 2016

x=189/62=3 3/62

Explanation:

As log_ba=loga/logb

log_5(x+3)=3+log_5(x-3) can be written as

log(x+3)/log5=3+log(x-3)/log5

As log5!=0, multiplying both sides by log5

log(x+3)=3log5+log(x-3) or

(x+3)=5^3(x-3)=125(x-3) or

x+3=125x-375 or

124x=378 and x=378/124=189/62=3 3/62