Find the x and y Intercepts f(x)=2 natural log of x-3

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

Find the x-intercepts.

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

$0 = 2 \ln (x - 3)$

Solve the equation.

Rewrite the equation as $2 \ln (x - 3) = 0$ .

$2 \ln (x - 3) = 0$

Divide each term in $2 \ln (x - 3) = 0$ by $2$ and simplify.

Divide each term in $2 \ln (x - 3) = 0$ by $2$ .

$\frac{2 \ln (x - 3)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 \ln (x - 3)}{2} = \frac{0}{2}$

Divide $\ln (x - 3)$ by $1$ .

$\ln (x - 3) = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$\ln (x - 3) = 0$

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

$e^{\ln (x - 3)} = e^{0}$

Rewrite $\ln (x - 3) = 0$ 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 $b^{y} = x$ .

$e^{0} = x - 3$

Solve for $x$ .

Rewrite the equation as $x - 3 = e^{0}$ .

$x - 3 = e^{0}$

Anything raised to $0$ is $1$ .

$x - 3 = 1$

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

$x = 1 + 3$

Add $1$ and $3$ .

$x = 4$

x-intercept(s) in point form.

x-intercept(s): $(4, 0)$

Find the y-intercepts.

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

$y = 2 \ln ((0) - 3)$

Solve the equation.

The natural logarithm of a negative number is undefined.

$y = Undefined$

Remove parentheses.

$y = 2 \ln ((0) - 3)$

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): $None$

List the intersections.

x-intercept(s): $(4, 0)$

y-intercept(s): $None$

Find the x and y Intercepts f(x)=2 natural log of x-3

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