Question

1. sketch the graph of $f(x) = \log_{3} x$. what is $b$ in this problem? $b = \underline{quadquad}$

Explanation:

Step1: Identify the base of log

The function is $f(x)=\log_{3}x$, so the base $b$ is the subscript of the logarithm.

Step2: Fill the table using log rules

Recall $\log_{b}x=y$ means $b^y=x$.

• For $f(x)=-1$: $3^{-1}=\frac{1}{3}$, so $x=\frac{1}{3}$
• For $x=1$: $\log_{3}1=0$ (since $3^0=1$)
• For $f(x)=1$: $3^1=3$, so $x=3$

Step3: Plot key points for the graph

Key points are $(\frac{1}{3}, -1)$, $(1, 0)$, $(3, 1)$. The graph of $\log_{3}x$ is increasing, has a vertical asymptote at $x=0$, and passes through these points.

Answer:

• $b=3$
• Completed table:

$x$	$f(x)=\log_{3}x$
$1$	$0$
$3$	$1$

• The graph of $f(x)=\log_{3}x$ has a vertical asymptote at $x=0$, increases from left to right, and passes through the points $(\frac{1}{3}, -1)$, $(1, 0)$, and $(3, 1)$.