Precalculus Examples

$30000 e^{\frac{\ln (2)}{19} \cdot (36)}$

Step 1

Rewrite $\frac{\ln (2)}{19}$ as $\frac{1}{19} \ln (2)$ .

$30000 e^{\frac{1}{19} \ln (2) \cdot 36}$

Step 2

Simplify $\frac{1}{19} \ln (2)$ by moving $\frac{1}{19}$ inside the logarithm.

$30000 e^{\ln (2^{\frac{1}{19}}) \cdot 36}$

Step 3

Multiply $\ln (2^{\frac{1}{19}}) \cdot 36$ .

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Step 3.1

Reorder $\ln (2^{\frac{1}{19}})$ and $36$ .

$30000 e^{36 \cdot \ln (2^{\frac{1}{19}})}$

Step 3.2

Simplify $36 \cdot \ln (2^{\frac{1}{19}})$ by moving $36$ inside the logarithm.

$30000 e^{\ln ({(2^{\frac{1}{19}})}^{36})}$

Step 4

Exponentiation and log are inverse functions.

$30000 {(2^{\frac{1}{19}})}^{36}$

Step 5

Multiply the exponents in ${(2^{\frac{1}{19}})}^{36}$ .

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Step 5.1

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

$30000 \cdot 2^{\frac{1}{19} \cdot 36}$

Step 5.2

Combine $\frac{1}{19}$ and $36$ .

$30000 \cdot 2^{\frac{36}{19}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$30000 \cdot 2^{\frac{36}{19}}$

Decimal Form:

$111556.24260100 \dots$