Question

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

Answer 1

`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`