Precalculus Examples

$\log_{a} (4 x^{6} y z^{3})$

Step 1

Rewrite $\log_{a} (4 x^{6} y z^{3})$ as $\log_{a} (4 x^{6} y) + \log_{a} (z^{3})$ .

$\log_{a} (4 x^{6} y) + \log_{a} (z^{3})$

Step 2

Rewrite $\log_{a} (4 x^{6} y)$ as $\log_{a} (4 x^{6}) + \log_{a} (y)$ .

$\log_{a} (4 x^{6}) + \log_{a} (y) + \log_{a} (z^{3})$

Step 3

Rewrite $\log_{a} (4 x^{6})$ as $\log_{a} (4) + \log_{a} (x^{6})$ .

$\log_{a} (4) + \log_{a} (x^{6}) + \log_{a} (y) + \log_{a} (z^{3})$

Step 4

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

$\log_{a} (4) + 6 \log_{a} (x) + \log_{a} (y) + \log_{a} (z^{3})$

Step 5

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

$\log_{a} (4) + 6 \log_{a} (x) + \log_{a} (y) + 3 \log_{a} (z)$

Step 6

Simplify each term.

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Step 6.1

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

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

Step 6.2

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

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