Question
Where does the logarithmic function y=log6x have a vertical asymptote?(1 point) Responses The logarithmic function y=log6x has no vertical asymptote. The logarithmic function y is equal to the log base 6 of x has no vertical asymptote. x=0 x is equal to 0 y=6 y is equal to 6 x=6
Answers
GPT-4o mini
The logarithmic function \( y = \log_6 x \) has a vertical asymptote at \( x = 0 \).
This is because the logarithm is undefined for non-positive values of \( x \) (i.e., \( x \leq 0 \)). As \( x \) approaches 0 from the right, the logarithmic function tends to negative infinity. Therefore, the correct response is:
**x = 0**.
This is because the logarithm is undefined for non-positive values of \( x \) (i.e., \( x \leq 0 \)). As \( x \) approaches 0 from the right, the logarithmic function tends to negative infinity. Therefore, the correct response is:
**x = 0**.