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

Question

Quizplus · Accepted Answer

For a logarithmic function $\log_b(x)$, the argument $x$ must be greater than zero. Given $f(x) = \log_5(x - 5)$, the argument $x - 5$ must be greater than zero. Solving $x - 5 > 0$ gives $x > 5$, which corresponds to the interval $(5, \infty)$.

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

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