Find the x and y Intercepts 10^x-100

$10^{x} - 100$

Step 1

Write $10^{x} - 100$ as an equation.

$y = 10^{x} - 100$

Step 2

Find the x-intercepts.

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

$0 = 10^{x} - 100$

Solve the equation.

Rewrite the equation as $10^{x} - 100 = 0$ .

$10^{x} - 100 = 0$

Add $100$ to both sides of the equation.

$10^{x} = 100$

Create equivalent expressions in the equation that all have equal bases.

$10^{x} = 10^{2}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Step 3

Find the y-intercepts.

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

$y = 10^{0} - 100$

Simplify $10^{0} - 100$ .

Anything raised to $0$ is $1$ .

$y = 1 - 100$

Subtract $100$ from $1$ .

$y = - 99$

y-intercept(s) in point form.

y-intercept(s): $(0, - 99)$

Step 4

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - 99)$

Step 5