Find the domain of the logarithmic function.
-$$f ( x ) = \log _ { 8 } ( x + 6 )$$
A) $( - \infty , 0 )$ or $( 0 , \infty )$
B) $( 8 , \infty )$
C) $( 6 , \infty )$
D) $( - 6 , \infty )$

Question

Quizplus · Accepted Answer

The argument of a logarithmic function must be greater than zero. Therefore, for $f(x) = \log_8(x + 6)$, the condition is $x + 6 > 0$, which simplifies to $x > -6$. This means the domain is all real numbers greater than -6, or $(-6, \infty)$.

Find the Domain of the Logarithmic Function f(x)=log⁡8(x+6)f ( x ) = \log _ { 8 } ( x + 6 )f(x)=log8​(x+6)

Find the Domain of the Logarithmic Function $f ( x ) = \log _ { 8 } ( x + 6 )$