Precalculus Examples

$\log (\sqrt{10000 z})$

Step 1

Rewrite $10000 z$ as ${(10^{2})}^{2} z$ .

Tap for more steps...

Step 1.1

Rewrite $10000$ as $100^{2}$ .

$\log (\sqrt{100^{2} z})$

Step 1.2

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

$\log (\sqrt{{(10^{2})}^{2} z})$

Step 2

Pull terms out from under the radical.

$\log (10^{2} \sqrt{z})$

Step 3

Rewrite $\log (10^{2} \sqrt{z})$ as $\log (10^{2}) + \log (\sqrt{z})$ .

$\log (10^{2}) + \log (\sqrt{z})$

Step 4

Use logarithm rules to move $2$ out of the exponent.

$2 \log (10) + \log (\sqrt{z})$

Step 5

Logarithm base $10$ of $10$ is $1$ .

$2 \cdot 1 + \log (\sqrt{z})$

Step 6

Multiply $2$ by $1$ .

$2 + \log (\sqrt{z})$