Finite Math Examples

$\log (3 x)$

Step 1

Set the argument in $\log (3 x)$ 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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Divide each term in $3 x > 0$ by $3$ .

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

Simplify the left side.

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Cancel the common factor of $3$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

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Divide $0$ by $3$ .

$x > 0$

Step 3

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

Interval Notation:

$(0, \infty)$

Set-Builder Notation:

${x | x > 0}$

Step 4