Precalculus Examples

$\log ({(\sqrt{100})}^{5})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{100}$ as $100^{\frac{1}{2}}$ .

$\log ({(100^{\frac{1}{2}})}^{5})$

Step 2

Expand $\log ({(100^{\frac{1}{2}})}^{5})$ by moving $5$ outside the logarithm.

$5 \log (100^{\frac{1}{2}})$

Step 3

Expand $\log (100^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$5 (\frac{1}{2} \log (100))$

Step 4

Logarithm base $10$ of $100$ is $2$ .

$5 (\frac{1}{2} \cdot 2)$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Cancel the common factor.

$5 (\frac{1}{2} \cdot 2)$

Step 5.2

Rewrite the expression.

$5 \cdot 1$

Step 6

Multiply $5$ by $1$ .

$5$