Precalculus Examples

$\log ({(\frac{1000}{a})}^{2})$

Step 1

Expand $\log ({(\frac{1000}{a})}^{2})$ by moving $2$ outside the logarithm.

$2 \log (\frac{1000}{a})$

Step 2

Rewrite $\log (\frac{1000}{a})$ as $\log (1000) - \log (a)$ .

$2 (\log (1000) - \log (a))$

Step 3

Logarithm base $10$ of $1000$ is $3$ .

$2 (3 - \log (a))$

Step 4

Apply the distributive property.

$2 \cdot 3 + 2 (- \log (a))$

Step 5

Multiply $2$ by $3$ .

$6 + 2 (- \log (a))$

Step 6

Multiply $- 1$ by $2$ .

$6 - 2 \log (a)$