Precalculus Examples

$\log_{3} (\frac{x^{2}}{81 y^{4}})$

Step 1

Rewrite $\log_{3} (\frac{x^{2}}{81 y^{4}})$ as $\log_{3} (x^{2}) - \log_{3} (81 y^{4})$ .

$\log_{3} (x^{2}) - \log_{3} (81 y^{4})$

Step 2

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

$2 \log_{3} (x) - \log_{3} (81 y^{4})$

Step 3

Rewrite $\log_{3} (81 y^{4})$ as $\log_{3} (81) + \log_{3} (y^{4})$ .

$2 \log_{3} (x) - (\log_{3} (81) + \log_{3} (y^{4}))$

Step 4

Expand $\log_{3} (y^{4})$ by moving $4$ outside the logarithm.

$2 \log_{3} (x) - (\log_{3} (81) + 4 \log_{3} (y))$

Step 5

Logarithm base $3$ of $81$ is $4$ .

$2 \log_{3} (x) - (4 + 4 \log_{3} (y))$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Apply the distributive property.

$2 \log_{3} (x) - 1 \cdot 4 - (4 \log_{3} (y))$

Step 6.2

Multiply $- 1$ by $4$ .

$2 \log_{3} (x) - 4 - (4 \log_{3} (y))$

Step 6.3

Multiply $4$ by $- 1$ .

$2 \log_{3} (x) - 4 - 4 \log_{3} (y)$