Precalculus Examples

$f (x) = \log (3 x - 2)$

Step 1

Set the argument in $\log (3 x - 2)$ greater than $0$ to find where the expression is defined.

$3 x - 2 > 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $2$ to both sides of the inequality.

$3 x > 2$

Step 2.2

Divide each term in $3 x > 2$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x > 2$ by $3$ .

$\frac{3 x}{3} > \frac{2}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} > \frac{2}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{2}{3}$

Step 3

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

Interval Notation:

$(\frac{2}{3}, \infty)$

Set-Builder Notation:

${x | x > \frac{2}{3}}$

Step 4