Precalculus Examples

$\log (\frac{a^{3}}{10 b})$

Step 1

Rewrite $\log (\frac{a^{3}}{10 b})$ as $\log (a^{3}) - \log (10 b)$ .

$\log (a^{3}) - \log (10 b)$

Step 2

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

$3 \log (a) - \log (10 b)$

Step 3

Rewrite $\log (10 b)$ as $\log (10) + \log (b)$ .

$3 \log (a) - (\log (10) + \log (b))$

Step 4

Logarithm base $10$ of $10$ is $1$ .

$3 \log (a) - (1 + \log (b))$

Step 5

Simplify each term.

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Step 5.1

Apply the distributive property.

$3 \log (a) - 1 \cdot 1 - \log (b)$

Step 5.2

Multiply $- 1$ by $1$ .

$3 \log (a) - 1 - \log (b)$