Trigonometry Examples

$\log_{5} (z \sqrt[3]{x \cdot y})$

Step 1

Rewrite $\log_{5} (z \sqrt[3]{x \cdot y})$ as $\log_{5} (z) + \log_{5} (\sqrt[3]{x \cdot y})$ .

$\log_{5} (z) + \log_{5} (\sqrt[3]{x \cdot y})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x \cdot y}$ as ${(x \cdot y)}^{\frac{1}{3}}$ .

$\log_{5} (z) + \log_{5} ({(x \cdot y)}^{\frac{1}{3}})$

Step 3

Expand $\log_{5} ({(x \cdot y)}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\log_{5} (z) + \frac{1}{3} \log_{5} (x \cdot y)$

Step 4

Rewrite $\log_{5} (x \cdot y)$ as $\log_{5} (x) + \log_{5} (y)$ .

$\log_{5} (z) + \frac{1}{3} (\log_{5} (x) + \log_{5} (y))$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\log_{5} (z) + \frac{1}{3} \log_{5} (x) + \frac{1}{3} \log_{5} (y)$

Step 5.2

Combine $\frac{1}{3}$ and $\log_{5} (x)$ .

$\log_{5} (z) + \frac{\log_{5} (x)}{3} + \frac{1}{3} \log_{5} (y)$

Step 5.3

Combine $\frac{1}{3}$ and $\log_{5} (y)$ .

$\log_{5} (z) + \frac{\log_{5} (x)}{3} + \frac{\log_{5} (y)}{3}$