Precalculus Examples

$\log_{3} (6 x y^{2})$

Step 1

Rewrite $\log_{3} (6 x y^{2})$ as $\log_{3} (6 x) + \log_{3} (y^{2})$ .

$\log_{3} (6 x) + \log_{3} (y^{2})$

Step 2

Rewrite $\log_{3} (6 x)$ as $\log_{3} (6) + \log_{3} (x)$ .

$\log_{3} (6) + \log_{3} (x) + \log_{3} (y^{2})$

Step 3

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

$\log_{3} (6) + \log_{3} (x) + 2 \log_{3} (y)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{3} (6)$ as $\log_{3} (2 (3))$ .

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

Step 4.2

Rewrite $\log_{3} (2 (3))$ as $\log_{3} (2) + \log_{3} (3)$ .

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

Step 4.3

Logarithm base $3$ of $3$ is $1$ .

$\log_{3} (2) + 1 + \log_{3} (x) + 2 \log_{3} (y)$