Precalculus Examples

$19 \log (\frac{3 \sqrt{m}}{n})$

Step 1

Rewrite $\log (\frac{3 \sqrt{m}}{n})$ as $\log (3 \sqrt{m}) - \log (n)$ .

$19 (\log (3 \sqrt{m}) - \log (n))$

Step 2

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

$19 (\log (3 m^{\frac{1}{2}}) - \log (n))$

Step 3

Rewrite $\log (3 m^{\frac{1}{2}})$ as $\log (3) + \log (m^{\frac{1}{2}})$ .

$19 (\log (3) + \log (m^{\frac{1}{2}}) - \log (n))$

Step 4

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

$19 (\log (3) + \frac{1}{2} \log (m) - \log (n))$

Step 5

Combine $\frac{1}{2}$ and $\log (m)$ .

$19 (\log (3) + \frac{\log (m)}{2} - \log (n))$

Step 6

Apply the distributive property.

$19 \log (3) + 19 \frac{\log (m)}{2} + 19 (- \log (n))$

Step 7

Simplify.

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Step 7.1

Combine $19$ and $\frac{\log (m)}{2}$ .

$19 \log (3) + \frac{19 \log (m)}{2} + 19 (- \log (n))$

Step 7.2

Multiply $- 1$ by $19$ .

$19 \log (3) + \frac{19 \log (m)}{2} - 19 \log (n)$