I need help with math problem!?

Question

the problem is g(x)=log(base 7)(x^2-49). I need to find the domain in interval notation. I need some help!

Answer 1

The domain of log(x) to any base is (0, infty), as negative numbers do not have logarithms.

log(x^2 - 49) is valid, therefore, provided:

x^2 - 49 > 0

x^2 > 49

x > 7 or x < - 7.

The domain of log[base 7](x^2 - 49) is (- infty, -7) U (7, infty).