Graph f(x) = natural log of x-2

$f (x) = \ln (x - 2)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

The vertical asymptote occurs at $x = 2$ .

Vertical Asymptote: $x = 2$

Step 2

Find the point at $x = 3$ .

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

$f (3) = \ln ((3) - 2)$

Simplify the result.

Subtract $2$ from $3$ .

$f (3) = \ln (1)$

The natural logarithm of $1$ is $0$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

$f (4) = \ln ((4) - 2)$

Simplify the result.

Subtract $2$ from $4$ .

$f (4) = \ln (2)$

The final answer is $\ln (2)$ .

$\ln (2)$

Convert $\ln (2)$ to decimal.

$y = 0.69314718$

Step 4

Find the point at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = \ln ((5) - 2)$

Simplify the result.

Subtract $2$ from $5$ .

$f (5) = \ln (3)$

The final answer is $\ln (3)$ .

$\ln (3)$

Convert $\ln (3)$ to decimal.

$y = 1.09861228$

Step 5

The log function can be graphed using the vertical asymptote at $x = 2$ and the points $(3, 0), (4, 0.69314718), (5, 1.09861228)$ .

Vertical Asymptote: $x = 2$

$\begin{array}{c} x & y \\ 3 & 0 \\ 4 & 0.693 \\ 5 & 1.099 \end{array}$

Step 6

Graph f(x) = natural log of x-2

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