Trigonometry Examples

$\log_{64} (\sqrt{2})$

Step 1

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

$\log_{64} (2^{\frac{1}{2}})$

Step 2

Expand $\log_{64} (2^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{64} (2)$

Step 3

Logarithm base $64$ of $2$ is $\frac{1}{6}$ .

$\frac{1}{2} \cdot \frac{1}{6}$

Step 4

Multiply $\frac{1}{2} \cdot \frac{1}{6}$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{1}{6}$ .

$\frac{1}{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$\frac{1}{12}$