Graph y = log base 5 of x-1

$y = \log_{5} (x - 1)$

Step 1

Find the asymptotes.

Set the argument of the logarithm equal to zero.

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The vertical asymptote occurs at $x = 1$ .

Vertical Asymptote: $x = 1$

Step 2

Find the point at $x = 2$ .

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

$f (2) = \log_{5} ((2) - 1)$

Simplify the result.

Subtract $1$ from $2$ .

$f (2) = \log_{5} (1)$

Logarithm base $5$ of $1$ is $0$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 6$ .

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

$f (6) = \log_{5} ((6) - 1)$

Simplify the result.

Subtract $1$ from $6$ .

$f (6) = \log_{5} (5)$

Logarithm base $5$ of $5$ is $1$ .

$f (6) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 3$ .

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

$f (3) = \log_{5} ((3) - 1)$

Simplify the result.

Subtract $1$ from $3$ .

$f (3) = \log_{5} (2)$

The final answer is $\log_{5} (2)$ .

$\log_{5} (2)$

Convert $\log_{5} (2)$ to decimal.

$y = 0.43067655$

Step 5

The log function can be graphed using the vertical asymptote at $x = 1$ and the points $(2, 0), (6, 1), (3, 0.43067655)$ .

Vertical Asymptote: $x = 1$

$\begin{array}{c} x & y \\ 2 & 0 \\ 3 & 0.431 \\ 6 & 1 \end{array}$

Step 6

Graph y = log base 5 of x-1

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