Final answer:
To find the vertical asymptote of a logarithmic function, set the argument of the log (inside the log function) equal to zero. The logarithm of zero is undefined, hence the function approaches negative infinity as the argument approaches zero, resulting in a vertical asymptote at x = 0.
Step-by-step explanation:
To find the vertical asymptote of a logarithmic function, you look at the argument of the logarithm, which is the input value inside the logarithm function. The vertical asymptote occurs where the argument of the log function equals zero because the logarithm of zero is undefined. Therefore, the correct approach is to set the argument of the log equal to zero. This is because a logarithm represents the power to which the base must be raised to obtain the number that is its argument, and there is no exponent that can make a base raised to it equal zero.
For example, considering the log function logb(x), we set the argument x equal to zero to find the vertical asymptote, but since no real number raised to any power gives zero, log functions will tend to negative infinity as the argument approaches zero from the positive side. Thus, x = 0 is where the function will have its vertical asymptote, assuming that the logarithm is defined for positive arguments as is usual.