Trigonometry Examples

$\log ({(\frac{100}{a})}^{4})$

Step 1

Expand $\log ({(\frac{100}{a})}^{4})$ by moving $4$ outside the logarithm.

$4 \log (\frac{100}{a})$

Step 2

Rewrite $\log (\frac{100}{a})$ as $\log (100) - \log (a)$ .

$4 (\log (100) - \log (a))$

Step 3

Logarithm base $10$ of $100$ is $2$ .

$4 (2 - \log (a))$

Step 4

Apply the distributive property.

$4 \cdot 2 + 4 (- \log (a))$

Step 5

Multiply $4$ by $2$ .

$8 + 4 (- \log (a))$

Step 6

Multiply $- 1$ by $4$ .

$8 - 4 \log (a)$