Precalculus Examples

$H (x) = \log_{5} (x^{3})$

Step 1

Set the argument in $\log_{5} (x^{3})$ greater than $0$ to find where the expression is defined.

$x^{3} > 0$

Step 2

Solve for $x$ .

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Step 2.1

Take the specified root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt[3]{x^{3}} > \sqrt[3]{0}$

Step 2.2

Simplify the equation.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Pull terms out from under the radical.

$x > \sqrt[3]{0}$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Simplify $\sqrt[3]{0}$ .

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Step 2.2.2.1.1

Rewrite $0$ as $0^{3}$ .

$x > \sqrt[3]{0^{3}}$

Step 2.2.2.1.2

Pull terms out from under the radical.

$x > 0$

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