Precalculus Examples

$\log (\sqrt[5]{10^{7}})$

Step 1

Raise $10$ to the power of $7$ .

$\log (\sqrt[5]{10000000})$

Step 2

Rewrite $10000000$ as $10^{5} \cdot 100$ .

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Step 2.1

Factor $100000$ out of $10000000$ .

$\log (\sqrt[5]{100000 (100)})$

Step 2.2

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

$\log (\sqrt[5]{10^{5} \cdot 100})$

$\log (\sqrt[5]{10^{5} \cdot 100})$

Step 3

Pull terms out from under the radical.

$\log (10 \sqrt[5]{100})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (10 \sqrt[5]{100})$

Decimal Form:

$1.4$

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