Precalculus Examples

$\log_{a} (4 x^{3} y)$

Step 1

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

$\log_{a} (4 x^{3}) + \log_{a} (y)$

Step 2

Rewrite $\log_{a} (4 x^{3})$ as $\log_{a} (4) + \log_{a} (x^{3})$ .

$\log_{a} (4) + \log_{a} (x^{3}) + \log_{a} (y)$

Step 3

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

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

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{a} (4)$ as $\log_{a} (2^{2})$ .

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

Step 4.2

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

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