Finite Math Examples

$m = c {(1 + i)}^{n}$

Step 1

Rewrite the equation as $c {(1 + i)}^{n} = m$ .

$c {(1 + i)}^{n} = m$

Step 2

Divide each term in $c {(1 + i)}^{n} = m$ by $c$ and simplify.

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Step 2.1

Divide each term in $c {(1 + i)}^{n} = m$ by $c$ .

$\frac{c {(1 + i)}^{n}}{c} = \frac{m}{c}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $c$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{c {(1 + i)}^{n}}{c} = \frac{m}{c}$

Step 2.2.1.2

Divide ${(1 + i)}^{n}$ by $1$ .

${(1 + i)}^{n} = \frac{m}{c}$

Step 3

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

$\ln ({(1 + i)}^{n}) = \ln (\frac{m}{c})$

Step 4

Expand $\ln ({(1 + i)}^{n})$ by moving $n$ outside the logarithm.

$n \ln (1 + i) = \ln (\frac{m}{c})$

Step 5

Divide each term in $n \ln (1 + i) = \ln (\frac{m}{c})$ by $\ln (1 + i)$ and simplify.

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Step 5.1

Divide each term in $n \ln (1 + i) = \ln (\frac{m}{c})$ by $\ln (1 + i)$ .

$\frac{n \ln (1 + i)}{\ln (1 + i)} = \frac{\ln (\frac{m}{c})}{\ln (1 + i)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1 + i)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{n \ln (1 + i)}{\ln (1 + i)} = \frac{\ln (\frac{m}{c})}{\ln (1 + i)}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{\ln (\frac{m}{c})}{\ln (1 + i)}$