Precalculus Examples

$10000 e^{(\frac{\ln (2)}{21}) \cdot 60}$

Step 1

Cancel the common factor of $3$ .

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Step 1.1

Factor $3$ out of $21$ .

$10000 e^{\frac{\ln (2)}{3 (7)} \cdot 60}$

Step 1.2

Factor $3$ out of $60$ .

$10000 e^{\frac{\ln (2)}{3 \cdot 7} \cdot (3 \cdot 20)}$

Step 1.3

Cancel the common factor.

$10000 e^{\frac{\ln (2)}{3 \cdot 7} \cdot (3 \cdot 20)}$

Step 1.4

Rewrite the expression.

$10000 e^{\frac{\ln (2)}{7} \cdot 20}$

Step 2

Combine $\frac{\ln (2)}{7}$ and $20$ .

$10000 e^{\frac{\ln (2) \cdot 20}{7}}$

Step 3

Reorder $\ln (2)$ and $20$ .

$10000 e^{\frac{20 \cdot \ln (2)}{7}}$

Step 4

Simplify $20 \cdot \ln (2)$ by moving $20$ inside the logarithm.

$10000 e^{\frac{\ln (2^{20})}{7}}$

Step 5

Rewrite $\frac{\ln (2^{20})}{7}$ as $\frac{1}{7} \ln (2^{20})$ .

$10000 e^{\frac{1}{7} \ln (2^{20})}$

Step 6

Simplify $\frac{1}{7} \ln (2^{20})$ by moving $\frac{1}{7}$ inside the logarithm.

$10000 e^{\ln ({(2^{20})}^{\frac{1}{7}})}$

Step 7

Exponentiation and log are inverse functions.

$10000 {(2^{20})}^{\frac{1}{7}}$

Step 8

Multiply the exponents in ${(2^{20})}^{\frac{1}{7}}$ .

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Step 8.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10000 \cdot 2^{20 (\frac{1}{7})}$

Step 8.2

Combine $20$ and $\frac{1}{7}$ .

$10000 \cdot 2^{\frac{20}{7}}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$10000 \cdot 2^{\frac{20}{7}}$

Decimal Form:

$72457.89314111 \dots$