Trigonometry Examples

$y = \log (5 x)$

Step 1

Set the argument in $\log (5 x)$ greater than $0$ to find where the expression is defined.

$5 x > 0$

Step 2

Divide each term in $5 x > 0$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 x > 0$ by $5$ .

$\frac{5 x}{5} > \frac{0}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} > \frac{0}{5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x > \frac{0}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $5$ .

$x > 0$

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