Calculus Examples

$60 e^{\frac{\ln (0.5)}{30} \cdot 110}$

Step 1

Cancel the common factor of $10$ .

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Step 1.1

Factor $10$ out of $30$ .

$60 e^{\frac{\ln (0.5)}{10 (3)} \cdot 110}$

Step 1.2

Factor $10$ out of $110$ .

$60 e^{\frac{\ln (0.5)}{10 \cdot 3} \cdot (10 \cdot 11)}$

Step 1.3

Cancel the common factor.

$60 e^{\frac{\ln (0.5)}{10 \cdot 3} \cdot (10 \cdot 11)}$

Step 1.4

Rewrite the expression.

$60 e^{\frac{\ln (0.5)}{3} \cdot 11}$

Step 2

Combine $\frac{\ln (0.5)}{3}$ and $11$ .

$60 e^{\frac{\ln (0.5) \cdot 11}{3}}$

Step 3

Reorder $\ln (0.5)$ and $11$ .

$60 e^{\frac{11 \cdot \ln (0.5)}{3}}$

Step 4

Simplify $11 \cdot \ln (0.5)$ by moving $11$ inside the logarithm.

$60 e^{\frac{\ln ({0.5}^{11})}{3}}$

Step 5

Rewrite $\frac{\ln ({0.5}^{11})}{3}$ as $\frac{1}{3} \ln ({0.5}^{11})$ .

$60 e^{\frac{1}{3} \ln ({0.5}^{11})}$

Step 6

Simplify $\frac{1}{3} \ln ({0.5}^{11})$ by moving $\frac{1}{3}$ inside the logarithm.

$60 e^{\ln ({({0.5}^{11})}^{\frac{1}{3}})}$

Step 7

Exponentiation and log are inverse functions.

$60 {({0.5}^{11})}^{\frac{1}{3}}$

Step 8

Multiply the exponents in ${({0.5}^{11})}^{\frac{1}{3}}$ .

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Step 8.1

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

$60 \cdot {0.5}^{11 (\frac{1}{3})}$

Step 8.2

Combine $11$ and $\frac{1}{3}$ .

$60 \cdot {0.5}^{\frac{11}{3}}$

Step 9

Raise $0.5$ to the power of $\frac{11}{3}$ .

$60 \cdot 0.07874506$

Step 10

Multiply $60$ by $0.07874506$ .

$4.72470393$