Precalculus Examples

$\log (6 x^{3} y^{4})$

Step 1

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

$\log (6 x^{3}) + \log (y^{4})$

Step 2

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

$\log (6) + \log (x^{3}) + \log (y^{4})$

Step 3

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

$\log (6) + 3 \log (x) + \log (y^{4})$

Step 4

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

$\log (6) + 3 \log (x) + 4 \log (y)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log (6)$ as $\log (2 (3))$ .

$\log (2 (3)) + 3 \log (x) + 4 \log (y)$

Step 5.2

Rewrite $\log (2 (3))$ as $\log (2) + \log (3)$ .

$\log (2) + \log (3) + 3 \log (x) + 4 \log (y)$