Precalculus Examples

$- 2 \log_{3} (\frac{1}{x}) + \frac{1}{3} \cdot (\log_{3} (\sqrt{x}))$

Step 1

Simplify $- 2 \log_{3} (\frac{1}{x})$ by moving $2$ inside the logarithm.

$- \log_{3} ({(\frac{1}{x})}^{2}) + \frac{1}{3} \cdot (\log_{3} (\sqrt{x}))$

Step 2

Apply the product rule to $\frac{1}{x}$ .

$- \log_{3} (\frac{1^{2}}{x^{2}}) + \frac{1}{3} \cdot (\log_{3} (\sqrt{x}))$

Step 3

One to any power is one.

$- \log_{3} (\frac{1}{x^{2}}) + \frac{1}{3} \cdot (\log_{3} (\sqrt{x}))$

Step 4

Simplify $\frac{1}{3} (\log_{3} (\sqrt{x}))$ by moving $\frac{1}{3}$ inside the logarithm.

$- \log_{3} (\frac{1}{x^{2}}) + \log_{3} ({\sqrt{x}}^{\frac{1}{3}})$