Find the x and y Intercepts y = log of 12x+7-3

$y = \log (12 x + 7) - 3$

Find the x-intercepts.

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

$0 = \log (12 x + 7) - 3$

Solve the equation.

Rewrite the equation as $\log (12 x + 7) - 3 = 0$ .

$\log (12 x + 7) - 3 = 0$

Add $3$ to both sides of the equation.

$\log (12 x + 7) = 3$

Rewrite $\log (12 x + 7) = 3$ 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 $b^{y} = x$ .

$10^{3} = 12 x + 7$

Solve for $x$ .

Rewrite the equation as $12 x + 7 = 10^{3}$ .

$12 x + 7 = 10^{3}$

Raise $10$ to the power of $3$ .

$12 x + 7 = 1000$

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

Subtract $7$ from both sides of the equation.

$12 x = 1000 - 7$

Subtract $7$ from $1000$ .

$12 x = 993$

Divide each term in $12 x = 993$ by $12$ and simplify.

Divide each term in $12 x = 993$ by $12$ .

$\frac{12 x}{12} = \frac{993}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{993}{12}$

Divide $x$ by $1$ .

$x = \frac{993}{12}$

Simplify the right side.

Cancel the common factor of $993$ and $12$ .

Factor $3$ out of $993$ .

$x = \frac{3 (331)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$x = \frac{3 \cdot 331}{3 \cdot 4}$

Cancel the common factor.

$x = \frac{3 \cdot 331}{3 \cdot 4}$

Rewrite the expression.

$x = \frac{331}{4}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{331}{4}, 0)$

Find the y-intercepts.

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

$y = \log (12 (0) + 7) - 3$

Solve the equation.

Remove parentheses.

$y = \log (12 (0) + 7) - 3$

Simplify each term.

Multiply $12$ by $0$ .

$y = \log (0 + 7) - 3$

Add $0$ and $7$ .

$y = \log (7) - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, \log (7) - 3)$

List the intersections.

x-intercept(s): $(\frac{331}{4}, 0)$

y-intercept(s): $(0, \log (7) - 3)$

Find the x and y Intercepts y = log of 12x+7-3

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