Basic Math Examples

$\frac{0.03}{500} \cdot (9000) = {(1 + 0.03)}^{n} - 1$

Step 1

Rewrite the equation as ${(1 + 0.03)}^{n} - 1 = \frac{0.03}{500} \cdot 9000$ .

${(1 + 0.03)}^{n} - 1 = \frac{0.03}{500} \cdot 9000$

Step 2

Add $1$ and $0.03$ .

${1.03}^{n} - 1 = \frac{0.03}{500} \cdot 9000$

Step 3

Simplify $\frac{0.03}{500} \cdot 9000$ .

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Step 3.1

Cancel the common factor of $500$ .

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Step 3.1.1

Factor $500$ out of $9000$ .

${1.03}^{n} - 1 = \frac{0.03}{500} \cdot (500 (18))$

Step 3.1.2

Cancel the common factor.

${1.03}^{n} - 1 = \frac{0.03}{500} \cdot (500 \cdot 18)$

Step 3.1.3

Rewrite the expression.

${1.03}^{n} - 1 = 0.03 \cdot 18$

Step 3.2

Multiply $0.03$ by $18$ .

${1.03}^{n} - 1 = 0.54$

Step 4

Move all terms not containing $n$ to the right side of the equation.

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Step 4.1

Add $1$ to both sides of the equation.

${1.03}^{n} = 0.54 + 1$

Step 4.2

Add $0.54$ and $1$ .

${1.03}^{n} = 1.54$

Step 5

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({1.03}^{n}) = \ln (1.54)$

Step 6

Expand $\ln ({1.03}^{n})$ by moving $n$ outside the logarithm.

$n \ln (1.03) = \ln (1.54)$

Step 7

Divide each term in $n \ln (1.03) = \ln (1.54)$ by $\ln (1.03)$ and simplify.

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Step 7.1

Divide each term in $n \ln (1.03) = \ln (1.54)$ by $\ln (1.03)$ .

$\frac{n \ln (1.03)}{\ln (1.03)} = \frac{\ln (1.54)}{\ln (1.03)}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $\ln (1.03)$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{n \ln (1.03)}{\ln (1.03)} = \frac{\ln (1.54)}{\ln (1.03)}$

Step 7.2.1.2

Divide $n$ by $1$ .

$n = \frac{\ln (1.54)}{\ln (1.03)}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$n = \frac{\ln (1.54)}{\ln (1.03)}$

Decimal Form:

$n = 14.60757485 \dots$