Find the x and y Intercepts y=-3 log base 2 of x+4+2

$y = - 3 \log_{2} (x + 4) + 2$

Step 1

Find the x-intercepts.

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

$0 = - 3 \log_{2} (x + 4) + 2$

Solve the equation.

Rewrite the equation as $- 3 \log_{2} (x + 4) + 2 = 0$ .

$- 3 \log_{2} (x + 4) + 2 = 0$

Subtract $2$ from both sides of the equation.

$- 3 \log_{2} (x + 4) = - 2$

Divide each term in $- 3 \log_{2} (x + 4) = - 2$ by $- 3$ and simplify.

Divide each term in $- 3 \log_{2} (x + 4) = - 2$ by $- 3$ .

$\frac{- 3 \log_{2} (x + 4)}{- 3} = \frac{- 2}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 \log_{2} (x + 4)}{- 3} = \frac{- 2}{- 3}$

Divide $\log_{2} (x + 4)$ by $1$ .

$\log_{2} (x + 4) = \frac{- 2}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

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

Rewrite $\log_{2} (x + 4) = \frac{2}{3}$ 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 $b^{y} = x$ .

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

Solve for $x$ .

Rewrite the equation as $x + 4 = 2^{\frac{2}{3}}$ .

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

Subtract $4$ from both sides of the equation.

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

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = - 3 \log_{2} ((0) + 4) + 2$

Solve the equation.

Remove parentheses.

$y = - 3 \log_{2} (0 + 4) + 2$

Remove parentheses.

$y = - 3 \log_{2} ((0) + 4) + 2$

Simplify $- 3 \log_{2} ((0) + 4) + 2$ .

Simplify each term.

Add $0$ and $4$ .

$y = - 3 \log_{2} (4) + 2$

Logarithm base $2$ of $4$ is $2$ .

$y = - 3 \cdot 2 + 2$

Multiply $- 3$ by $2$ .

$y = - 6 + 2$

Add $- 6$ and $2$ .

$y = - 4$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts y=-3 log base 2 of x+4+2

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