1 - log(1.3263318809610271764974967102508e-4319) / log(2)=?

asked by guest
on Sep 21, 2024 at 5:16 am



You asked:

Evaluate the expression: \(1 - \frac{\log\left( 1.3263318809610271764974967102508 e - 4319 \right)}{\log\left( 2 \right)}\)

MathBot Answer:

\[1 - \frac{\log\left( 1.3263318809610271764974967102508 e - 4319 \right)}{\log\left( 2 \right)} = 1 - \frac{\log{\left(4319 - \frac{3315829702402567941243741775627 e}{2500000000000000000000000000000} \right)} + i \pi}{\log{\left(2 \right)}}\]

\[\begin{aligned}1 - \frac{\log\left( 1.3263318809610271764974967102508 e - 4319 \right)}{\log\left( 2 \right)}& = 1 - \log{\left(\left(1 + \frac{3263318809610271764974967102508}{10000000000000000000000000000000}\right) \cdot e - 4319 \right)} \cdot \frac{1}{\log{\left(2 \right)}}\\& = 1 - \log{\left(\left(1 + \frac{815829702402567941243741775627}{2500000000000000000000000000000}\right) \cdot e - 4319 \right)} \cdot \frac{1}{\log{\left(2 \right)}}\\& = 1 - \log{\left(\frac{3315829702402567941243741775627}{2500000000000000000000000000000} \cdot e - 4319 \right)} \cdot \frac{1}{\log{\left(2 \right)}}\\& = 1 - \log{\left(-4319 + \frac{3315829702402567941243741775627}{2500000000000000000000000000000} \cdot e \right)} \cdot \frac{1}{\log{\left(2 \right)}}\\& = 1 - \left(\pi \cdot i + \log{\left(4319 - \frac{3315829702402567941243741775627}{2500000000000000000000000000000} \cdot e \right)}\right) \cdot \frac{1}{\log{\left(2 \right)}}\\& = 1 - \frac{1}{\log{\left(2 \right)}} \cdot \left(\pi \cdot i + \log{\left(4319 - \frac{3315829702402567941243741775627}{2500000000000000000000000000000} \cdot e \right)}\right)\end{aligned}\]

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

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