Precalculus Examples

$\frac{\ln (2)}{12 \ln (1 + \frac{0.04}{12})}$

Step 1

Simplify $12 \ln (1 + \frac{0.04}{12})$ by moving $12$ inside the logarithm.

$\frac{\ln (2)}{\ln ({(1 + \frac{0.04}{12})}^{12})}$

Step 2

Simplify the denominator.

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Step 2.1

Divide $0.04$ by $12$ .

$\frac{\ln (2)}{\ln ({(1 + 0.00\overline{3})}^{12})}$

Step 2.2

Add $1$ and $0.00\overline{3}$ .

$\frac{\ln (2)}{\ln ({1.00\overline{3}}^{12})}$

Step 2.3

Raise $1.00\overline{3}$ to the power of $12$ .

$\frac{\ln (2)}{\ln (1.04074154)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (2)}{\ln (1.04074154)}$

Decimal Form:

$17.35754462 \dots$