Precalculus Examples

$\log_{6} (6 \sqrt{6})$

Step 1

Rewrite $\log_{6} (6 \sqrt{6})$ as $\log_{6} (6) + \log_{6} (\sqrt{6})$ .

$\log_{6} (6) + \log_{6} (\sqrt{6})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

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

Step 3

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

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

Step 4

Logarithm base $6$ of $6$ is $1$ .

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

Step 5

Logarithm base $6$ of $6$ is $1$ .

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

Step 6

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

$1 + \frac{1}{2}$

Step 7

Write $1$ as a fraction with a common denominator.

$\frac{2}{2} + \frac{1}{2}$

Step 8

Combine the numerators over the common denominator.

$\frac{2 + 1}{2}$

Step 9

Add $2$ and $1$ .

$\frac{3}{2}$