Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }$$
A) $( - \infty , 9 )$ or $( 9 , \infty )$
B) $( - \infty , 0 )$ or $( 0 , \infty )$
C) $( - 9 , \infty )$
D) $( 9 , \infty )$ (9

Question

Quizplus · Accepted Answer

For the logarithmic function $\log_5(x-9)^2$, the argument $(x-9)^2$ must be greater than 0 because the logarithm of a non-positive number is undefined. The square of any real number except 0 is positive, so $x-9$ can be any real number except 9. Therefore, the domain is all real numbers except 9, which is option A: $(- \infty , 9 )$ or $( 9 , \infty )$.

Find the Domain of the Logarithmic Function f(x)=log⁡5(x−9)2f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }f(x)=log5​(x−9)2

Find the Domain of the Logarithmic Function $f ( x ) = \log _ { 5 } ( x - 9 ) ^ { 2 }$