Precalculus Examples

$\log (\frac{1 \sqrt{1000}}{1000})$

Step 1

Multiply $\sqrt{1000}$ by $1$ .

$\log (\frac{\sqrt{1000}}{1000})$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1000$ as $10^{2} \cdot 10$ .

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Step 2.1.1

Factor $100$ out of $1000$ .

$\log (\frac{\sqrt{100 (10)}}{1000})$

Step 2.1.2

Rewrite $100$ as $10^{2}$ .

$\log (\frac{\sqrt{10^{2} \cdot 10}}{1000})$

$\log (\frac{\sqrt{10^{2} \cdot 10}}{1000})$

Step 2.2

Pull terms out from under the radical.

$\log (\frac{10 \sqrt{10}}{1000})$

$\log (\frac{10 \sqrt{10}}{1000})$

Step 3

Cancel the common factor of $10$ and $1000$ .

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Step 3.1

Factor $10$ out of $10 \sqrt{10}$ .

$\log (\frac{10 (\sqrt{10})}{1000})$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $10$ out of $1000$ .

$\log (\frac{10 \sqrt{10}}{10 \cdot 100})$

Step 3.2.2

Cancel the common factor.

$\log (\frac{10 \sqrt{10}}{10 \cdot 100})$

Step 3.2.3

Rewrite the expression.

$\log (\frac{\sqrt{10}}{100})$

$\log (\frac{\sqrt{10}}{100})$

$\log (\frac{\sqrt{10}}{100})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{\sqrt{10}}{100})$

Decimal Form:

$- 1.5$

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