How do you solve log_4 (x^2 - 9) - log_4 (x+3) = 3?

1 Answer
Dec 25, 2015

x=67

Explanation:

color(white)xxlog_4 (x^2-9)-log_4(x+3)=3

The logarithm of the ratio of two numbers is the difference of the logarithms.
=>log_4 ((x^2-9)/(x+3))=3

DOTS RULE:
An expression in the form of a squared number less another squared number is called the difference of two squares.
=>log_4 (((x-3)(x+3))/(x+3))=3

=>log_4 (x-3)=3
=>4^3=x-3
=>x-3+3=64+3
=>x=67