Algebra Examples

$\log (\frac{1}{10} \sqrt{1000})$

Step 1

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

Tap for more steps...

Step 1.1

Factor $100$ out of $1000$ .

$\log (\frac{1}{10} \cdot \sqrt{100 (10)})$

Step 1.2

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

$\log (\frac{1}{10} \cdot \sqrt{10^{2} \cdot 10})$

$\log (\frac{1}{10} \cdot \sqrt{10^{2} \cdot 10})$

Step 2

Pull terms out from under the radical.

$\log (\frac{1}{10} \cdot (10 \sqrt{10}))$

Step 3

Cancel the common factor of $10$ .

Tap for more steps...

Step 3.1

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

$\log (\frac{1}{10} \cdot (10 (\sqrt{10})))$

Step 3.2

Cancel the common factor.

$\log (\frac{1}{10} \cdot (10 \sqrt{10}))$

Step 3.3

Rewrite the expression.

$\log (\sqrt{10})$

$\log (\sqrt{10})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (\sqrt{10})$

Decimal Form:

$0.5$

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