Examine the logarithmic function f(x).
f(x)=log1/3x
The function f(x) has a vertical asymptote at x= [blank] −−−−−−.
Enter your answer as an integer that correctly fills in the blank. For example, if the vertical asymptote is at x=100,
enter this: 100
The vertical asymptote of the logarithmic function f(x) = log1/3x is at x = 0.
To find the vertical asymptote of the logarithmic function f(x) = log(1/3)x, we need to consider the domain of the function.
In general, the vertical asymptote of a logarithmic function occurs when the argument (input) of the logarithm is zero or negative. However, since we have a fraction as the base of the logarithm in this case, we need to determine the value of x that makes (1/3)x equal to zero.
(1/3)x = 0
To solve for x, we can use the property of exponents, which states that any number raised to the power of zero is equal to 1. Applying this property, we have:
(1/3)x = 0
(1/3)x = (1/3)0
Since the bases are equal, the exponents must also be equal:
x = 0
Therefore, the vertical asymptote of the function f(x) = log(1/3)x is x = 0.