Find the domain of the logarithmic function. Write your answer in interval notation.
-$$f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }$$
A) $( 8 , \infty )$
B) $( - 8 , \infty )$
C) $( - \infty , 0 ) \cup ( 0 , \infty )$
D) $( - \infty , 8 ) \cup ( 8 , \infty )$

Question

Quizplus · Accepted Answer

The argument of the logarithmic function, $(x - 8)^2$, must be greater than 0 because the logarithm of a non-positive number is undefined. Squaring any real number except 0 gives a positive result, so $x - 8$ can be any real number except 8. Therefore, the domain is all real numbers except 8, which is $( - \infty , 8 ) \cup ( 8 , \infty )$.

Find the Domain of the Logarithmic Function f(x)=log⁡4(x−8)2f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }f(x)=log4​(x−8)2

Find the Domain of the Logarithmic Function $f ( x ) = \log _ { 4 } ( x - 8 ) ^ { 2 }$