Precalculus Examples

$\frac{\log (\frac{1}{8}) \cdot 2}{3}$

Step 1

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

$\frac{(\log (1) - \log (8)) \cdot 2}{3}$

Step 2

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

$\frac{(0 - \log (8)) \cdot 2}{3}$

Step 3

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

$\frac{(0 - \log (2^{3})) \cdot 2}{3}$

Step 4

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

$\frac{(0 - (3 \log (2))) \cdot 2}{3}$

Step 5

Multiply $3$ by $- 1$ .

$\frac{(0 - 3 \log (2)) \cdot 2}{3}$

Step 6

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

$\frac{- 3 \log (2) \cdot 2}{3}$

Step 7

Cancel the common factor of $- 3$ and $3$ .

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Step 7.1

Factor $3$ out of $- 3 \log (2) \cdot 2$ .

$\frac{3 (- \log (2) \cdot 2)}{3}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $3$ .

$\frac{3 (- \log (2) \cdot 2)}{3 (1)}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (- \log (2) \cdot 2)}{3 \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{- \log (2) \cdot 2}{1}$

Step 7.2.4

Divide $- \log (2) \cdot 2$ by $1$ .

$- \log (2) \cdot 2$

Step 8

Multiply $2$ by $- 1$ .

$- 2 \log (2)$