Precalculus Examples

$\log_{6} (12 x y^{3})$

Step 1

Rewrite $\log_{6} (12 x y^{3})$ as $\log_{6} (12 x) + \log_{6} (y^{3})$ .

$\log_{6} (12 x) + \log_{6} (y^{3})$

Step 2

Rewrite $\log_{6} (12 x)$ as $\log_{6} (12) + \log_{6} (x)$ .

$\log_{6} (12) + \log_{6} (x) + \log_{6} (y^{3})$

Step 3

Expand $\log_{6} (y^{3})$ by moving $3$ outside the logarithm.

$\log_{6} (12) + \log_{6} (x) + 3 \log_{6} (y)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{6} (12)$ as $\log_{6} (2^{2} \cdot 3)$ .

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

Step 4.2

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

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

Step 4.3

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

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