Find the x and y Intercepts f(x)=e^x-5

$f (x) = e^{x} - 5$

Step 1

Find the x-intercepts.

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

$0 = e^{x} - 5$

Solve the equation.

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

$e^{x} - 5 = 0$

Add $5$ to both sides of the equation.

$e^{x} = 5$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

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

Expand the left side.

Expand $\ln (e^{x})$ by moving $x$ outside the logarithm.

$x \ln (e) = \ln (5)$

The natural logarithm of $e$ is $1$ .

$x \cdot 1 = \ln (5)$

Multiply $x$ by $1$ .

$x = \ln (5)$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = e^{0} - 5$

Simplify $e^{0} - 5$ .

Anything raised to $0$ is $1$ .

$y = 1 - 5$

Subtract $5$ from $1$ .

$y = - 4$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4