Precalculus Examples

$\log (\frac{1}{4}) (\frac{1}{256})$

Step 1

Rewrite $\log (\frac{1}{4})$ as $\log (1) - \log (4)$ .

$(\log (1) - \log (4)) \frac{1}{256}$

Step 2

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

$(0 - \log (4)) \frac{1}{256}$

Step 3

Rewrite $\log (4)$ as $\log (2^{2})$ .

$(0 - \log (2^{2})) \frac{1}{256}$

Step 4

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

$(0 - (2 \log (2))) \frac{1}{256}$

Step 5

Multiply $2$ by $- 1$ .

$(0 - 2 \log (2)) \frac{1}{256}$

Step 6

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

$- 2 \log (2) \frac{1}{256}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

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

$2 (- \log (2)) \frac{1}{256}$

Step 7.2

Factor $2$ out of $256$ .

$2 (- \log (2)) \frac{1}{2 (128)}$

Step 7.3

Cancel the common factor.

$2 (- \log (2)) \frac{1}{2 \cdot 128}$

Step 7.4

Rewrite the expression.

$- \log (2) \frac{1}{128}$

Step 8

Combine $\frac{1}{128}$ and $\log (2)$ .

$- \frac{\log (2)}{128}$