Precalculus Examples

$\log_{4} (\frac{19 \sqrt{m}}{n})$

Step 1

Rewrite $\log_{4} (\frac{19 \sqrt{m}}{n})$ as $\log_{4} (19 \sqrt{m}) - \log_{4} (n)$ .

$\log_{4} (19 \sqrt{m}) - \log_{4} (n)$

Step 2

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

$\log_{4} (19 m^{\frac{1}{2}}) - \log_{4} (n)$

Step 3

Rewrite $\log_{4} (19 m^{\frac{1}{2}})$ as $\log_{4} (19) + \log_{4} (m^{\frac{1}{2}})$ .

$\log_{4} (19) + \log_{4} (m^{\frac{1}{2}}) - \log_{4} (n)$

Step 4

Expand $\log_{4} (m^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\log_{4} (19) + \frac{1}{2} \log_{4} (m) - \log_{4} (n)$

Step 5

Combine $\frac{1}{2}$ and $\log_{4} (m)$ .

$\log_{4} (19) + \frac{\log_{4} (m)}{2} - \log_{4} (n)$