Precalculus Examples

$\log (\sqrt[5]{10^{9}})$

Step 1

Raise $10$ to the power of $9$ .

$\log (\sqrt[5]{1000000000})$

Step 2

Rewrite $1000000000$ as $10^{5} \cdot 10000$ .

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Step 2.1

Factor $100000$ out of $1000000000$ .

$\log (\sqrt[5]{100000 (10000)})$

Step 2.2

Rewrite $100000$ as $10^{5}$ .

$\log (\sqrt[5]{10^{5} \cdot 10000})$

$\log (\sqrt[5]{10^{5} \cdot 10000})$

Step 3

Pull terms out from under the radical.

$\log (10 \sqrt[5]{10000})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (10 \sqrt[5]{10000})$

Decimal Form:

$1.8$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$