Precalculus Examples

$\log (\frac{a}{b^{3} c^{7}})$

Step 1

Rewrite $\log (\frac{a}{b^{3} c^{7}})$ as $\log (a) - \log (b^{3} c^{7})$ .

$\log (a) - \log (b^{3} c^{7})$

Step 2

Rewrite $\log (b^{3} c^{7})$ as $\log (b^{3}) + \log (c^{7})$ .

$\log (a) - (\log (b^{3}) + \log (c^{7}))$

Step 3

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

$\log (a) - (3 \log (b) + \log (c^{7}))$

Step 4

Expand $\log (c^{7})$ by moving $7$ outside the logarithm.

$\log (a) - (3 \log (b) + 7 \log (c))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$\log (a) - (3 \log (b)) - (7 \log (c))$

Step 5.2

Multiply $3$ by $- 1$ .

$\log (a) - 3 \log (b) - (7 \log (c))$

Step 5.3

Multiply $7$ by $- 1$ .

$\log (a) - 3 \log (b) - 7 \log (c)$