Given the parent functions f(x) = log₃(5x - 5) and g(x) = log₃(x - 1), what is f(x) - g(x)?

Solution:

Given parent functions are f(x) = log₃(5x - 5) and g(x) = log₃(x - 1)

f(x) - g(x) = log\(_3\)(5x-5) - log\(_3\)(x-1)

But from basic laws of logarithm

log (a) - log(b) = log(a /b)

f(x) - g (x) = log\(_3\)(5x-5) - log\(_3\)(x-1)

=\(log_{3}\frac{5x-5}{x-1}\)

=\(log_{3}\frac{5(x-1)}{x-1}\)

= \(log_{3}\)5

If f(x) = log\(_3\)(5x-5) - log\(_3\)(x-1) then f(x) - g(x) = 5.

Given the parent functions f(x) = log3 (5x - 5) and g(x) = log3 (x - 1), what is f(x) - g(x)?

Summary:

If f(x) = log₃(5x - 5) and g(x) = log₃(x - 1) then f(x) - g (x) =  log₃(5x - 5) - log₃(x - 1) is 5.