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

$y = \log (3 x + 4) + 2$

Find the x-intercepts.

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

$0 = \log (3 x + 4) + 2$

Solve the equation.

Rewrite the equation as $\log (3 x + 4) + 2 = 0$ .

$\log (3 x + 4) + 2 = 0$

Subtract $2$ from both sides of the equation.

$\log (3 x + 4) = - 2$

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

$10^{- 2} = 3 x + 4$

Solve for $x$ .

Rewrite the equation as $3 x + 4 = 10^{- 2}$ .

$3 x + 4 = 10^{- 2}$

Simplify $10^{- 2}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 x + 4 = \frac{1}{10^{2}}$

Raise $10$ to the power of $2$ .

$3 x + 4 = \frac{1}{100}$

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

Subtract $4$ from both sides of the equation.

$3 x = \frac{1}{100} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$3 x = \frac{1}{100} - 4 \cdot \frac{100}{100}$

Combine $- 4$ and $\frac{100}{100}$ .

$3 x = \frac{1}{100} + \frac{- 4 \cdot 100}{100}$

Combine the numerators over the common denominator.

$3 x = \frac{1 - 4 \cdot 100}{100}$

Simplify the numerator.

Multiply $- 4$ by $100$ .

$3 x = \frac{1 - 400}{100}$

Subtract $400$ from $1$ .

$3 x = \frac{- 399}{100}$

Move the negative in front of the fraction.

$3 x = - \frac{399}{100}$

Divide each term in $3 x = - \frac{399}{100}$ by $3$ and simplify.

Divide each term in $3 x = - \frac{399}{100}$ by $3$ .

$\frac{3 x}{3} = \frac{- \frac{399}{100}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \frac{399}{100}}{3}$

Divide $x$ by $1$ .

$x = \frac{- \frac{399}{100}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{399}{100} \cdot \frac{1}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{399}{100}$ into the numerator.

$x = \frac{- 399}{100} \cdot \frac{1}{3}$

Factor $3$ out of $- 399$ .

$x = \frac{3 (- 133)}{100} \cdot \frac{1}{3}$

Cancel the common factor.

$x = \frac{3 \cdot - 133}{100} \cdot \frac{1}{3}$

Rewrite the expression.

$x = \frac{- 133}{100}$

Move the negative in front of the fraction.

$x = - \frac{133}{100}$

x-intercept(s) in point form.

x-intercept(s): $(- \frac{133}{100}, 0)$

Find the y-intercepts.

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

$y = \log (3 (0) + 4) + 2$

Solve the equation.

Remove parentheses.

$y = \log (3 (0) + 4) + 2$

Simplify each term.

Multiply $3$ by $0$ .

$y = \log (0 + 4) + 2$

Add $0$ and $4$ .

$y = \log (4) + 2$

y-intercept(s) in point form.

y-intercept(s): $(0, \log (4) + 2)$

List the intersections.

x-intercept(s): $(- \frac{133}{100}, 0)$

y-intercept(s): $(0, \log (4) + 2)$

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

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