Precalculus Examples

$- \frac{\ln (1 - \frac{24000 (0.19)}{12 (500)})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $24000$ and $12$ .

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Step 1.1.1

Factor $12$ out of $24000 (0.19)$ .

$- \frac{\ln (1 - \frac{12 (2000 \cdot 0.19)}{12 (500)})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Cancel the common factor.

$- \frac{\ln (1 - \frac{12 (2000 \cdot 0.19)}{12 \cdot 500})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.1.2.2

Rewrite the expression.

$- \frac{\ln (1 - \frac{2000 \cdot 0.19}{500})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.2

Cancel the common factor of $2000$ and $500$ .

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Step 1.2.1

Factor $500$ out of $2000 \cdot 0.19$ .

$- \frac{\ln (1 - \frac{500 (4 \cdot 0.19)}{500})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $500$ out of $500$ .

$- \frac{\ln (1 - \frac{500 (4 \cdot 0.19)}{500 (1)})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.2.2.2

Cancel the common factor.

$- \frac{\ln (1 - \frac{500 (4 \cdot 0.19)}{500 \cdot 1})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.2.2.3

Rewrite the expression.

$- \frac{\ln (1 - \frac{4 \cdot 0.19}{1})}{12 \ln (1 + \frac{0.19}{12})}$

Step 1.2.2.4

Divide $4 \cdot 0.19$ by $1$ .

$- \frac{\ln (1 - (4 \cdot 0.19))}{12 \ln (1 + \frac{0.19}{12})}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $- 1 \cdot 4 \cdot 0.19$ .

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Step 2.1.1

Multiply $- 1$ by $4$ .

$- \frac{\ln (1 - 4 \cdot 0.19)}{12 \ln (1 + \frac{0.19}{12})}$

Step 2.1.2

Multiply $- 4$ by $0.19$ .

$- \frac{\ln (1 - 0.76)}{12 \ln (1 + \frac{0.19}{12})}$

Step 2.2

Subtract $0.76$ from $1$ .

$- \frac{\ln (0.24)}{12 \ln (1 + \frac{0.19}{12})}$

Step 3

Simplify $12 \ln (1 + \frac{0.19}{12})$ by moving $12$ inside the logarithm.

$- \frac{\ln (0.24)}{\ln ({(1 + \frac{0.19}{12})}^{12})}$

Step 4

Simplify the denominator.

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Step 4.1

Divide $0.19$ by $12$ .

$- \frac{\ln (0.24)}{\ln ({(1 + 0.0158\overline{3})}^{12})}$

Step 4.2

Add $1$ and $0.0158\overline{3}$ .

$- \frac{\ln (0.24)}{\ln ({1.0158\overline{3}}^{12})}$

Step 4.3

Raise $1.0158\overline{3}$ to the power of $12$ .

$- \frac{\ln (0.24)}{\ln (1.20745099)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\ln (0.24)}{\ln (1.20745099)}$

Decimal Form:

$7.57044620 \dots$