Basic Math Examples

$13000 = 6500 {(1 + \frac{0.037}{4})}^{4 (t)}$

Step 1

Rewrite the equation as $6500 {(1 + \frac{0.037}{4})}^{4 t} = 13000$ .

$6500 {(1 + \frac{0.037}{4})}^{4 t} = 13000$

Step 2

Simplify.

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Step 2.1

Divide $0.037$ by $4$ .

$6500 {(1 + 0.00925)}^{4 t} = 13000$

Step 2.2

Add $1$ and $0.00925$ .

$6500 \cdot {1.00925}^{4 t} = 13000$

Step 3

Divide each term in $6500 \cdot {1.00925}^{4 t} = 13000$ by $6500$ and simplify.

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Step 3.1

Divide each term in $6500 \cdot {1.00925}^{4 t} = 13000$ by $6500$ .

$\frac{6500 \cdot {1.00925}^{4 t}}{6500} = \frac{13000}{6500}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6500$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6500 \cdot {1.00925}^{4 t}}{6500} = \frac{13000}{6500}$

Step 3.2.1.2

Divide ${1.00925}^{4 t}$ by $1$ .

${1.00925}^{4 t} = \frac{13000}{6500}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $13000$ by $6500$ .

${1.00925}^{4 t} = 2$

Step 4

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

$\ln ({1.00925}^{4 t}) = \ln (2)$

Step 5

Expand $\ln ({1.00925}^{4 t})$ by moving $4 t$ outside the logarithm.

$4 t \ln (1.00925) = \ln (2)$

Step 6

Divide each term in $4 t \ln (1.00925) = \ln (2)$ by $4 \ln (1.00925)$ and simplify.

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Step 6.1

Divide each term in $4 t \ln (1.00925) = \ln (2)$ by $4 \ln (1.00925)$ .

$\frac{4 t \ln (1.00925)}{4 \ln (1.00925)} = \frac{\ln (2)}{4 \ln (1.00925)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $4$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{4 t \ln (1.00925)}{4 \ln (1.00925)} = \frac{\ln (2)}{4 \ln (1.00925)}$

Step 6.2.1.2

Rewrite the expression.

$\frac{t \ln (1.00925)}{\ln (1.00925)} = \frac{\ln (2)}{4 \ln (1.00925)}$

Step 6.2.2

Cancel the common factor of $\ln (1.00925)$ .

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Step 6.2.2.1

Cancel the common factor.

$\frac{t \ln (1.00925)}{\ln (1.00925)} = \frac{\ln (2)}{4 \ln (1.00925)}$

Step 6.2.2.2

Divide $t$ by $1$ .

$t = \frac{\ln (2)}{4 \ln (1.00925)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\ln (2)}{4 \ln (1.00925)}$

Decimal Form:

$t = 18.82021801 \dots$