Basic Math Examples

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

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

Step 1

Rewrite the equation as

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

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

{(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

$1$ and

0.03

$0.03$ .

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

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

Step 3

Simplify

\frac{0.03}{500} \cdot 9000

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

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Step 3.1

Cancel the common factor of

500

$500$ .

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Step 3.1.1

Factor

500

$500$ out of

9000

$9000$ .

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

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

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:

$n = 14.60757485 \dots$