Finite Math Examples

$\frac{\ln (3 x)}{x - 1}$

Step 1

Set the argument in $\ln (3 x)$ greater than $0$ to find where the expression is defined.

$3 x > 0$

Step 2

Divide each term in $3 x > 0$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 x > 0$ by $3$ .

$\frac{3 x}{3} > \frac{0}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{0}{3}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x > \frac{0}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $3$ .

$x > 0$

Step 3

Set the denominator in $\frac{\ln (3 x)}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Step 4

Add $1$ to both sides of the equation.

$x = 1$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(0, 1) \cup (1, \infty)$

Set-Builder Notation:

${x | x > 0, x \neq 1}$

Step 6