Question

graph the following logarithmic function by first placing its vertical asymptote.

\\y = \log_{\frac{1}{3}} (x)\\

Explanation:

Step1: Identify the vertical asymptote

$$x = 0$$

Step2: Find the x-intercept

$$y = \log_{\frac{1}{3}}(1) = 0 \implies (1, 0)$$

Step3: Find a second point

$$y = \log_{\frac{1}{3}}(3) = -1 \implies (3, -1)$$

Step4: Find a third point

$$y = \log_{\frac{1}{3}}(9) = -2 \implies (9, -2)$$

Answer:

The vertical asymptote is at \(x = 0\), and the graph passes through the points \((1, 0)\), \((3, -1)\), and \((9, -2)\).