Basic Math Examples

$N = \frac{\ln (200 \div (200 - 6000 \cdot 0.18 \div 12))}{\ln (1 + 0.18 \div 12)}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $6000$ and $12$ .

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Step 1.1.1

Factor $12$ out of $6000 \cdot 0.18$ .

$N = \frac{\ln (200 \div (200 - 12 (500 \cdot 0.18) \div 12))}{\ln (1 + 0.18 \div 12)}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $12$ out of $12$ .

$N = \frac{\ln (200 \div (200 - 12 (500 \cdot 0.18) \div 12 (1)))}{\ln (1 + 0.18 \div 12)}$

Step 1.1.2.2

Cancel the common factor.

$N = \frac{\ln (200 \div (200 - 12 (500 \cdot 0.18) \div 12 \cdot 1))}{\ln (1 + 0.18 \div 12)}$

Step 1.1.2.3

Rewrite the expression.

$N = \frac{\ln (200 \div (200 - \frac{500 \cdot 0.18}{1}))}{\ln (1 + 0.18 \div 12)}$

Step 1.1.2.4

Divide $500 \cdot 0.18$ by $1$ .

$N = \frac{\ln (200 \div (200 - (500 \cdot 0.18)))}{\ln (1 + 0.18 \div 12)}$

Step 1.2

Cancel the common factor of $200$ and $200 - (500 \cdot 0.18)$ .

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Step 1.2.1

Reorder terms.

$N = \frac{\ln (200 \div (- 1 \cdot 0.18 \cdot 500 + 200))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.2

Factor $2$ out of $200$ .

$N = \frac{\ln (2 (100) \div (- 1 \cdot 0.18 \cdot 500 + 200))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.3

Cancel the common factors.

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Step 1.2.3.1

Factor $2$ out of $- 1 \cdot 0.18 \cdot 500$ .

$N = \frac{\ln (2 (100) \div (2 (- 1 \cdot 0.09 \cdot 500) + 200))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.3.2

Factor $2$ out of $200$ .

$N = \frac{\ln (2 \cdot 100 \div (2 (- 1 \cdot 0.09 \cdot 500) + 2 \cdot 100))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.3.3

Factor $2$ out of $2 (- 1 \cdot 0.09 \cdot 500) + 2 (100)$ .

$N = \frac{\ln (2 (100) \div 2 (- 1 \cdot 0.09 \cdot 500 + 100))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.3.4

Cancel the common factor.

$N = \frac{\ln (2 \cdot 100 \div 2 (- 1 \cdot 0.09 \cdot 500 + 100))}{\ln (1 + 0.18 \div 12)}$

Step 1.2.3.5

Rewrite the expression.

$N = \frac{\ln (\frac{100}{- 1 \cdot 0.09 \cdot 500 + 100})}{\ln (1 + 0.18 \div 12)}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 1 \cdot 0.09 \cdot 500$ .

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Step 2.1.1

Multiply $- 1$ by $0.09$ .

$N = \frac{\ln (\frac{100}{- 0.09 \cdot 500 + 100})}{\ln (1 + 0.18 \div 12)}$

Step 2.1.2

Multiply $- 0.09$ by $500$ .

$N = \frac{\ln (\frac{100}{- 45 + 100})}{\ln (1 + 0.18 \div 12)}$

Step 2.2

Add $- 45$ and $100$ .

$N = \frac{\ln (\frac{100}{55})}{\ln (1 + 0.18 \div 12)}$

Step 3

Cancel the common factor of $100$ and $55$ .

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Step 3.1

Factor $5$ out of $100$ .

$N = \frac{\ln (\frac{5 (20)}{55})}{\ln (1 + 0.18 \div 12)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $55$ .

$N = \frac{\ln (\frac{5 \cdot 20}{5 \cdot 11})}{\ln (1 + 0.18 \div 12)}$

Step 3.2.2

Cancel the common factor.

$N = \frac{\ln (\frac{5 \cdot 20}{5 \cdot 11})}{\ln (1 + 0.18 \div 12)}$

Step 3.2.3

Rewrite the expression.

$N = \frac{\ln (\frac{20}{11})}{\ln (1 + 0.18 \div 12)}$

Step 4

Simplify the denominator.

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Step 4.1

Divide $0.18$ by $12$ .

$N = \frac{\ln (\frac{20}{11})}{\ln (1 + 0.015)}$

Step 4.2

Add $1$ and $0.015$ .

$N = \frac{\ln (\frac{20}{11})}{\ln (1.015)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$N = \frac{\ln (\frac{20}{11})}{\ln (1.015)}$

Decimal Form:

$N = 40.15397680 \dots$