Precalculus Examples

$\log (\frac{6 x^{5}}{y})$

Step 1

Rewrite $\log (\frac{6 x^{5}}{y})$ as $\log (6 x^{5}) - \log (y)$ .

$\log (6 x^{5}) - \log (y)$

Step 2

Rewrite $\log (6 x^{5})$ as $\log (6) + \log (x^{5})$ .

$\log (6) + \log (x^{5}) - \log (y)$

Step 3

Expand $\log (x^{5})$ by moving $5$ outside the logarithm.

$\log (6) + 5 \log (x) - \log (y)$

Step 4

Simplify each term.

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Step 4.1

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

$\log (2 (3)) + 5 \log (x) - \log (y)$

Step 4.2

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

$\log (2) + \log (3) + 5 \log (x) - \log (y)$