Precalculus Examples

$\log_{6} (w^{3} \sqrt{u})$

Step 1

Rewrite $\log_{6} (w^{3} \sqrt{u})$ as $\log_{6} (w^{3}) + \log_{6} (\sqrt{u})$ .

$\log_{6} (w^{3}) + \log_{6} (\sqrt{u})$

Step 2

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

$\log_{6} (w^{3}) + \log_{6} (u^{\frac{1}{2}})$

Step 3

Expand $\log_{6} (w^{3})$ by moving $3$ outside the logarithm.

$3 \log_{6} (w) + \log_{6} (u^{\frac{1}{2}})$

Step 4

Expand $\log_{6} (u^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$3 \log_{6} (w) + \frac{1}{2} \log_{6} (u)$

Step 5

Combine $\frac{1}{2}$ and $\log_{6} (u)$ .

$3 \log_{6} (w) + \frac{\log_{6} (u)}{2}$