Precalculus Examples

$\frac{\log (2)}{12 \log (1 + \frac{0.05}{12})}$

Step 1

Simplify $12 \log (1 + \frac{0.05}{12})$ by moving $12$ inside the logarithm.

$\frac{\log (2)}{\log ({(1 + \frac{0.05}{12})}^{12})}$

Step 2

Simplify the denominator.

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Step 2.1

Divide $0.05$ by $12$ .

$\frac{\log (2)}{\log ({(1 + 0.0041\overline{6})}^{12})}$

Step 2.2

Add $1$ and $0.0041\overline{6}$ .

$\frac{\log (2)}{\log ({1.0041\overline{6}}^{12})}$

Step 2.3

Raise $1.0041\overline{6}$ to the power of $12$ .

$\frac{\log (2)}{\log (1.05116189)}$

Step 2.4

Log base $10$ of $1.05116189$ is approximately $0.02166961$ .

$\frac{\log (2)}{0.02166961}$

Step 3

Log base $10$ of $2$ is approximately $0.30102999$ .

$\frac{0.30102999}{0.02166961}$

Step 4

Divide $0.30102999$ by $0.02166961$ .

$13.89180472$