Certainly! Let's solve for the vertical asymptote of the function [tex]\(y = \log(x - 4)\)[/tex].
1. Understand the argument of the logarithmic function:
The function [tex]\( y = \log(x - 4) \)[/tex] is defined only when the argument inside the logarithm, [tex]\( x - 4 \)[/tex], is positive. This means:
[tex]\[
x - 4 > 0
\][/tex]
Therefore,
[tex]\[
x > 4
\][/tex]
2. Vertical asymptote:
A vertical asymptote occurs where the argument of the logarithm goes to zero. For the function [tex]\( y = \log(x - 4) \)[/tex], the argument inside the logarithm is [tex]\( x - 4 \)[/tex].
3. Set the argument equal to zero:
To find the vertical asymptote, set the argument [tex]\( x - 4 \)[/tex] equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = 0
\][/tex]
[tex]\[
x = 4
\][/tex]
Thus, the vertical asymptote of the function [tex]\( y = \log(x - 4) \)[/tex] is at:
[tex]\[
x = 4
\][/tex]
Hence, the final answer is [tex]\( \boxed{4} \)[/tex].
