Graph f(x) = log base b of x

$f (x) = \log_{b} (x)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x = 0$

The vertical asymptote occurs at $x = 0$ .

Vertical Asymptote: $x = 0$

Step 2

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = \log_{b} (1)$

Simplify the result.

Logarithm base $b$ of $1$ is $0$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = \log_{b} (2)$

The final answer is $\log_{b} (2)$ .

$\log_{b} (2)$

Convert $\log_{b} (2)$ to decimal.

$y = \log_{b} (2)$

Step 4

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = \log_{b} (3)$

The final answer is $\log_{b} (3)$ .

$\log_{b} (3)$

Convert $\log_{b} (3)$ to decimal.

$y = \log_{b} (3)$

Step 5

The log function can be graphed using the vertical asymptote at $x = 0$ and the points $(1, 0), (2, \log_{b} (2)), (3, \log_{b} (3))$ .

Vertical Asymptote: $x = 0$

$\begin{array}{c} x & y \\ 1 & 0 \\ 2 & \log_{b} (2) \\ 3 & \log_{b} (3) \end{array}$

Step 6