Graph log of x-4

$\log (x - 4)$

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

The vertical asymptote occurs at $x = 4$ .

Vertical Asymptote: $x = 4$

Find the point at $x = 5$ .

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

$f (5) = \log ((5) - 4)$

Simplify the result.

Subtract $4$ from $5$ .

$f (5) = \log (1)$

Logarithm base $10$ of $1$ is $0$ .

$f (5) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 14$ .

Replace the variable $x$ with $14$ in the expression.

$f (14) = \log ((14) - 4)$

Simplify the result.

Subtract $4$ from $14$ .

$f (14) = \log (10)$

Logarithm base $10$ of $10$ is $1$ .

$f (14) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Find the point at $x = 6$ .

Replace the variable $x$ with $6$ in the expression.

$f (6) = \log ((6) - 4)$

Simplify the result.

Subtract $4$ from $6$ .

$f (6) = \log (2)$

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

$\log (2)$

Convert $\log (2)$ to decimal.

$y = 0.30102999$

The log function can be graphed using the vertical asymptote at $x = 4$ and the points $(5, 0), (14, 1), (6, 0.30102999)$ .

Vertical Asymptote: $x = 4$

$\begin{array}{c} x & y \\ 5 & 0 \\ 6 & 0.301 \\ 14 & 1 \end{array}$