Question

the equation $y = \log(x + 3)$ has a vertical asymptote at $x = \square$ question help: video

Explanation:

Step1: Recall the vertical asymptote of logarithmic functions

For a logarithmic function of the form \( y = \log_b(u) \), the vertical asymptote occurs where the argument \( u = 0 \) (since the logarithm is undefined for non - positive arguments, and as \( u \) approaches 0 from the positive side, the function values approach negative infinity).

Step2: Set the argument of the given logarithmic function to zero

The given function is \( y=\log(x + 3) \). Here, the argument \( u=x + 3 \). We set \( x+3=0 \).

Step3: Solve for x

To solve the equation \( x + 3=0 \), we subtract 3 from both sides of the equation. So, \( x=-3 \).

Answer:

\(-3\)