50,000⋅e^(-(-ln⁡(0.7)/2)5)

asked by guest
on Jan 21, 2025 at 6:09 am



You asked:

Evaluate the expression: \(50,000 {e}^{-\left( \frac{-\ln\left( 0.7 \right)}{2} \cdot 5 \right)}\)

MathBot Answer:

\[50,000 {e}^{-\left( \frac{-\ln\left( 0.7 \right)}{2} \cdot 5 \right)} = 2450 \sqrt{70} \approx 20498.17065008485092546521463173709349\]

\[\begin{aligned}50,000 {e}^{-\left( \frac{-\ln\left( 0.7 \right)}{2} \cdot 5 \right)}& = 50000 \cdot e^{- - \cdot \log{\left(\frac{7}{10} \right)} \cdot \frac{5}{2}}\\& = 50000 \cdot e^{- - \log{\left(\frac{7}{10} \right)} \cdot \frac{5}{2}}\\& = 50000 \cdot e^{- - \frac{1}{2} \cdot \log{\left(\frac{7}{10} \right)} \cdot 5}\\& = 50000 \cdot e^{- - \frac{5}{2} \cdot \log{\left(\frac{7}{10} \right)}}\\& = 50000 \cdot e^{\frac{5}{2} \cdot \log{\left(\frac{7}{10} \right)}}\\& = 50000 \cdot \frac{49}{1000} \cdot \sqrt{70}\\& = 2450 \cdot \sqrt{70}\end{aligned}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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