Trigonometry Examples

$\log_{8} (50)$

Step 1

Rewrite $\log_{8} (50)$ as $\log_{8} (2 \cdot 5^{2})$ .

$\log_{8} (2 \cdot 5^{2})$

Step 2

Rewrite $\log_{8} (2 \cdot 5^{2})$ as $\log_{8} (2) + \log_{8} (5^{2})$ .

$\log_{8} (2) + \log_{8} (5^{2})$

Step 3

Simplify each term.

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Step 3.1

Logarithm base $8$ of $2$ is $\frac{1}{3}$ .

$\frac{1}{3} + \log_{8} (5^{2})$

Step 3.2

Expand $\log_{8} (5^{2})$ by moving $2$ outside the logarithm.

$\frac{1}{3} + 2 \log_{8} (5)$