Precalculus Examples

$\log (\frac{1}{8}) (a - b)$

Step 1

Rewrite $\log (\frac{1}{8})$ as $\log (1) - \log (8)$ .

$(\log (1) - \log (8)) (a - b)$

Step 2

Logarithm base $10$ of $1$ is $0$ .

$(0 - \log (8)) (a - b)$

Step 3

Rewrite $\log (8)$ as $\log (2^{3})$ .

$(0 - \log (2^{3})) (a - b)$

Step 4

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$(0 - (3 \log (2))) (a - b)$

Step 5

Multiply $3$ by $- 1$ .

$(0 - 3 \log (2)) (a - b)$

Step 6

Subtract $3 \log (2)$ from $0$ .

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

Step 7

Apply the distributive property.

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

Step 8

Multiply $- 1$ by $- 3$ .

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

Step 9

Reorder factors in $- 3 \log (2) a + 3 \log (2) b$ .

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