Find the x and y Intercepts f(x) = natural log of x-1-1

$f (x) = \ln (x - 1) - 1$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \ln (x - 1) - 1$

Solve the equation.

Rewrite the equation as $\ln (x - 1) - 1 = 0$ .

$\ln (x - 1) - 1 = 0$

Add $1$ to both sides of the equation.

$\ln (x - 1) = 1$

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (x - 1)} = e^{1}$

Rewrite $\ln (x - 1) = 1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{1} = x - 1$

Solve for $x$ .

Rewrite the equation as $x - 1 = e^{1}$ .

$x - 1 = e$

Add $1$ to both sides of the equation.

$x = e + 1$

x-intercept(s) in point form.

x-intercept(s): $(e + 1, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \ln ((0) - 1) - 1$

Solve the equation.

The natural logarithm of a negative number is undefined.

$y = Undefined$

Remove parentheses.

$y = \ln ((0) - 1) - 1$

The equation cannot be solved because it is undefined.

$Undefined$

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(e + 1, 0)$

y-intercept(s): $None$

Step 4

Find the x and y Intercepts f(x) = natural log of x-1-1

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