Precalculus Examples

$\log (\frac{c^{3}}{a^{9} b^{3}})$

Step 1

Rewrite $\log (\frac{c^{3}}{a^{9} b^{3}})$ as $\log (c^{3}) - \log (a^{9} b^{3})$ .

$\log (c^{3}) - \log (a^{9} b^{3})$

Step 2

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

$3 \log (c) - \log (a^{9} b^{3})$

Step 3

Rewrite $\log (a^{9} b^{3})$ as $\log (a^{9}) + \log (b^{3})$ .

$3 \log (c) - (\log (a^{9}) + \log (b^{3}))$

Step 4

Expand $\log (a^{9})$ by moving $9$ outside the logarithm.

$3 \log (c) - (9 \log (a) + \log (b^{3}))$

Step 5

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

$3 \log (c) - (9 \log (a) + 3 \log (b))$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Apply the distributive property.

$3 \log (c) - (9 \log (a)) - (3 \log (b))$

Step 6.2

Multiply $9$ by $- 1$ .

$3 \log (c) - 9 \log (a) - (3 \log (b))$

Step 6.3

Multiply $3$ by $- 1$ .

$3 \log (c) - 9 \log (a) - 3 \log (b)$