Find the x and y Intercepts y = log of 7x+3-2

$y = \log (7 x + 3) - 2$

Find the x-intercepts.

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

$0 = \log (7 x + 3) - 2$

Solve the equation.

Rewrite the equation as $\log (7 x + 3) - 2 = 0$ .

$\log (7 x + 3) - 2 = 0$

Add $2$ to both sides of the equation.

$\log (7 x + 3) = 2$

Rewrite $\log (7 x + 3) = 2$ 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 $b^{y} = x$ .

$10^{2} = 7 x + 3$

Solve for $x$ .

Rewrite the equation as $7 x + 3 = 10^{2}$ .

$7 x + 3 = 10^{2}$

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

$7 x + 3 = 100$

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

Subtract $3$ from both sides of the equation.

$7 x = 100 - 3$

Subtract $3$ from $100$ .

$7 x = 97$

Divide each term in $7 x = 97$ by $7$ and simplify.

Divide each term in $7 x = 97$ by $7$ .

$\frac{7 x}{7} = \frac{97}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{97}{7}$

Divide $x$ by $1$ .

$x = \frac{97}{7}$

x-intercept(s) in point form.

x-intercept(s): $(\frac{97}{7}, 0)$

Find the y-intercepts.

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

$y = \log (7 (0) + 3) - 2$

Solve the equation.

Remove parentheses.

$y = \log (7 (0) + 3) - 2$

Simplify each term.

Multiply $7$ by $0$ .

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

Add $0$ and $3$ .

$y = \log (3) - 2$

y-intercept(s) in point form.

y-intercept(s): $(0, \log (3) - 2)$

List the intersections.

x-intercept(s): $(\frac{97}{7}, 0)$

y-intercept(s): $(0, \log (3) - 2)$

Find the x and y Intercepts y = log of 7x+3-2

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