Find the x and y Intercepts y=4 log of x+6

$y = 4 \log (x + 6)$

Find the x-intercepts.

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

$0 = 4 \log (x + 6)$

Solve the equation.

Rewrite the equation as $4 \log (x + 6) = 0$ .

$4 \log (x + 6) = 0$

Divide each term in $4 \log (x + 6) = 0$ by $4$ and simplify.

Divide each term in $4 \log (x + 6) = 0$ by $4$ .

$\frac{4 \log (x + 6)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \log (x + 6)}{4} = \frac{0}{4}$

Divide $\log (x + 6)$ by $1$ .

$\log (x + 6) = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$\log (x + 6) = 0$

Rewrite $\log (x + 6) = 0$ 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 $b^{y} = x$ .

$10^{0} = x + 6$

Solve for $x$ .

Rewrite the equation as $x + 6 = 10^{0}$ .

$x + 6 = 10^{0}$

Anything raised to $0$ is $1$ .

$x + 6 = 1$

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

Subtract $6$ from both sides of the equation.

$x = 1 - 6$

Subtract $6$ from $1$ .

$x = - 5$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = 4 \log ((0) + 6)$

Solve the equation.

Remove parentheses.

$y = 4 \log (0 + 6)$

Remove parentheses.

$y = 4 \log ((0) + 6)$

Simplify $4 \log ((0) + 6)$ .

Add $0$ and $6$ .

$y = 4 \log (6)$

Simplify $4 \log (6)$ by moving $4$ inside the logarithm.

$y = \log (6^{4})$

Raise $6$ to the power of $4$ .

$y = \log (1296)$

y-intercept(s) in point form.

y-intercept(s): $(0, \log (1296))$

List the intersections.

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

y-intercept(s): $(0, \log (1296))$

Find the x and y Intercepts y=4 log of x+6

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