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The equation [tex]$y=\log (x-4)$[/tex] has a vertical asymptote at:

[tex]x = \square[/tex]

Sagot :

GinnyAnswer
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].
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