Algebra Examples

$y = 3 (4^{x}) - 2$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = 3 (4^{x}) - 2$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $3 \cdot 4^{x} - 2 = 0$ .

$3 \cdot 4^{x} - 2 = 0$

Step 1.2.2

Add $2$ to both sides of the equation.

$3 \cdot 4^{x} = 2$

Step 1.2.3

Divide each term in $3 \cdot 4^{x} = 2$ by $3$ and simplify.

Tap for more steps...

Step 1.2.3.1

Divide each term in $3 \cdot 4^{x} = 2$ by $3$ .

$\frac{3 \cdot 4^{x}}{3} = \frac{2}{3}$

Step 1.2.3.2

Simplify the left side.

Tap for more steps...

Step 1.2.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{3 \cdot 4^{x}}{3} = \frac{2}{3}$

Step 1.2.3.2.1.2

Divide $4^{x}$ by $1$ .

$4^{x} = \frac{2}{3}$

Step 1.2.4

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

$\ln (4^{x}) = \ln (\frac{2}{3})$

Step 1.2.5

Expand $\ln (4^{x})$ by moving $x$ outside the logarithm.

$x \ln (4) = \ln (\frac{2}{3})$

Step 1.2.6

Divide each term in $x \ln (4) = \ln (\frac{2}{3})$ by $\ln (4)$ and simplify.

Tap for more steps...

Step 1.2.6.1

Divide each term in $x \ln (4) = \ln (\frac{2}{3})$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (\frac{2}{3})}{\ln (4)}$

Step 1.2.6.2

Simplify the left side.

Tap for more steps...

Step 1.2.6.2.1

Cancel the common factor of $\ln (4)$ .

Tap for more steps...

Step 1.2.6.2.1.1

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (\frac{2}{3})}{\ln (4)}$

Step 1.2.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{2}{3})}{\ln (4)}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{\ln (\frac{2}{3})}{\ln (4)}, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = 3 (4^{0}) - 2$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Multiply $3$ by $4^{0}$ .

$y = 3 \cdot 4^{0} - 2$

Step 2.2.2

Remove parentheses.

$y = 3 (4^{0}) - 2$

Step 2.2.3

Simplify $3 (4^{0}) - 2$ .

Tap for more steps...

Step 2.2.3.1

Simplify each term.

Tap for more steps...

Step 2.2.3.1.1

Anything raised to $0$ is $1$ .

$y = 3 \cdot 1 - 2$

Step 2.2.3.1.2

Multiply $3$ by $1$ .

$y = 3 - 2$

Step 2.2.3.2

Subtract $2$ from $3$ .

$y = 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $(\frac{\ln (\frac{2}{3})}{\ln (4)}, 0)$

y-intercept(s): $(0, 1)$

Step 4