Precalculus Examples

$y = \log (\frac{x}{7})$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = \log (\frac{x}{7})$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\log (\frac{x}{7}) = 0$ .

$\log (\frac{x}{7}) = 0$

Step 1.2.2

Rewrite $\log (\frac{x}{7}) = 0$ 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 $b^{y} = x$ .

$10^{0} = \frac{x}{7}$

Step 1.2.3

Solve for $x$ .

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Step 1.2.3.1

Rewrite the equation as $\frac{x}{7} = 10^{0}$ .

$\frac{x}{7} = 10^{0}$

Step 1.2.3.2

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \cdot 10^{0}$

Step 1.2.3.3

Simplify both sides of the equation.

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Step 1.2.3.3.1

Simplify the left side.

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Step 1.2.3.3.1.1

Cancel the common factor of $7$ .

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Step 1.2.3.3.1.1.1

Cancel the common factor.

$7 \frac{x}{7} = 7 \cdot 10^{0}$

Step 1.2.3.3.1.1.2

Rewrite the expression.

$x = 7 \cdot 10^{0}$

Step 1.2.3.3.2

Simplify the right side.

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Step 1.2.3.3.2.1

Convert $7 \cdot 10^{0}$ from scientific notation.

$x = 7$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(7, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = \log (\frac{0}{7})$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = \log (\frac{0}{7})$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Divide $0$ by $7$ .

$y = \log (0)$

Step 2.2.2.2

The equation cannot be solved because it is undefined.

$Undefined$

Step 2.3

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(7, 0)$

y-intercept(s): $None$

Step 4