Find the domain of the function $k ( x ) = \log _ { 8 } ( 4 - x )$ .
A) $( 4 , \infty )$
B) $( - \infty , 8 )$
C) $( - 4 , \infty )$
D) $( - \infty , 4 )$
E) $( 8 , \infty )$

Question

Quizplus · Accepted Answer

For the logarithmic function $k(x) = \log_8(4-x)$ to be defined, the argument $4-x$ must be greater than 0. Solving the inequality $4-x > 0$ gives $x < 4$. Therefore, the domain is all real numbers less than 4, which is $(-\infty, 4)$.

Find the Domain of the Function k(x)=log⁡8(4−x)k ( x ) = \log _ { 8 } ( 4 - x )k(x)=log8​(4−x)

Find the Domain of the Function $k ( x ) = \log _ { 8 } ( 4 - x )$