Find the x and y Intercepts f(x)=- natural log of x+5

$f (x) = - \ln (x + 5)$

Step 1

Find the x-intercepts.

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

$0 = - \ln (x + 5)$

Solve the equation.

Rewrite the equation as $- \ln (x + 5) = 0$ .

$- \ln (x + 5) = 0$

Divide each term in $- \ln (x + 5) = 0$ by $- 1$ and simplify.

Divide each term in $- \ln (x + 5) = 0$ by $- 1$ .

$\frac{- \ln (x + 5)}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\ln (x + 5)}{1} = \frac{0}{- 1}$

Divide $\ln (x + 5)$ by $1$ .

$\ln (x + 5) = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$\ln (x + 5) = 0$

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

$e^{\ln (x + 5)} = e^{0}$

Rewrite $\ln (x + 5) = 0$ 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 $b^{y} = x$ .

$e^{0} = x + 5$

Solve for $x$ .

Rewrite the equation as $x + 5 = e^{0}$ .

$x + 5 = e^{0}$

Anything raised to $0$ is $1$ .

$x + 5 = 1$

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

Subtract $5$ from both sides of the equation.

$x = 1 - 5$

Subtract $5$ from $1$ .

$x = - 4$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = - \ln ((0) + 5)$

Solve the equation.

Remove parentheses.

$y = - \ln (0 + 5)$

Remove parentheses.

$y = - \ln ((0) + 5)$

Add $0$ and $5$ .

$y = - \ln (5)$

y-intercept(s) in point form.

y-intercept(s): $(0, - \ln (5))$

Step 3

List the intersections.

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

y-intercept(s): $(0, - \ln (5))$

Step 4

Find the x and y Intercepts f(x)=- natural log of x+5

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