Precalculus Examples

$\frac{\log_{3} (e^{- 2})}{\log_{3} (e^{- \frac{1}{3}})}$

Step 1

Expand $\log_{3} (e^{- 2})$ by moving $- 2$ outside the logarithm.

$\frac{- 2 \log_{3} (e)}{\log_{3} (e^{- \frac{1}{3}})}$

Step 2

Expand $\log_{3} (e^{- \frac{1}{3}})$ by moving $- \frac{1}{3}$ outside the logarithm.

$\frac{- 2 \log_{3} (e)}{- \frac{1}{3} \log_{3} (e)}$

Step 3

Cancel the common factor of $\log_{3} (e)$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{- 2 \log_{3} (e)}{- \frac{1}{3} \log_{3} (e)}$

Step 3.2

Rewrite the expression.

$\frac{- 2}{- \frac{1}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- 2 (- 1 \cdot 3)$

Step 5

Multiply $- 2 (- 1 \cdot 3)$ .

Tap for more steps...

Step 5.1

Multiply $- 1$ by $3$ .

$- 2 \cdot - 3$

Step 5.2

Multiply $- 2$ by $- 3$ .

$6$