Calculus Examples

$y = \log (2 x - 12)$

Step 1

Set the argument in $\log (2 x - 12)$ greater than $0$ to find where the expression is defined.

$2 x - 12 > 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Add $12$ to both sides of the inequality.

$2 x > 12$

Step 2.2

Divide each term in $2 x > 12$ by $2$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $2 x > 12$ by $2$ .

$\frac{2 x}{2} > \frac{12}{2}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} > \frac{12}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{12}{2}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $12$ by $2$ .

$x > 6$

Step 3

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

Interval Notation:

$(6, \infty)$

Set-Builder Notation:

${x | x > 6}$

Step 4