Given the parent functions f(x) = log₂(3x - 9) and g(x) = log₂(x - 3), what is f(x) - g(x)?

Solution:

Given parent functions are f(x) = log2 (3x - 9 ) and g(x) = log2 (x - 3)

\(f(x) - g(x) = [log_{2}^{(3x-9)}-log_{2}^{(x -3)}]\)

But according to property of the log law for division is subtract

\(log(a) - log(b) = log(\frac{a}{b})\)

\(f(x) - g(x) = log_{2}^{3x-9} - log_{2}^{x-3}\)

\(\Rightarrow log_{2}^{3x-9} - log_{2}^{x-3} =log_{2}^{\frac{3x-9}{x-3}}\)

\(\Rightarrow log_{2}^{3x-9} - log_{2}^{x-3} =log_{2}^{\frac{3(x-3)}{x-3}}\)

\(\Rightarrow log_{2}^{3x-9} - log_{2}^{x-3} =log_{2}^{3}\)

\(\therefore if f(x)=log_{2}^{3x-9} and g(x) = log_{2}^{x-3} then f(x)-g(x)=log_{2}^{3}\)