Precalculus Examples

$\log_{17} (\frac{5 \sqrt{12}}{n^{2} m})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$\log_{17} (\frac{5 \sqrt{4 (3)}}{n^{2} m})$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\log_{17} (\frac{5 \sqrt{2^{2} \cdot 3}}{n^{2} m})$

Step 1.2

Pull terms out from under the radical.

$\log_{17} (\frac{5 \cdot 2 \sqrt{3}}{n^{2} m})$

Step 1.3

Multiply $5$ by $2$ .

$\log_{17} (\frac{10 \sqrt{3}}{n^{2} m})$

Step 2

Rewrite $\log_{17} (\frac{10 \sqrt{3}}{n^{2} m})$ using the change of base formula.

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Step 2.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 2.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\frac{10 \sqrt{3}}{n^{2} m})}{\log (17)}$