Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 4 } ( x - 2 )$$
A) $( 2 , \infty )$
B) $( - \infty , 0 )$ or $( 0 , \infty )$
C) $( - \infty , 2 )$ or $( 2 , \infty )$
D) $( - 2 , \infty )$

Question

Quizplus · Accepted Answer

For a logarithmic function $\log_b(x)$, the argument $x$ must be greater than 0. In the given function $f(x) = \log_4(x - 2)$, the argument is $x - 2$. Therefore, $x - 2 > 0$, which simplifies to $x > 2$. This means the domain of the function is all real numbers greater than 2, which is represented by the interval $(2, \infty)$.

Find the Domain of the Logarithmic Function f(x)=log⁡4(x−2)f ( x ) = \log _ { 4 } ( x - 2 )f(x)=log4​(x−2)

Find the Domain of the Logarithmic Function $f ( x ) = \log _ { 4 } ( x - 2 )$