e^(-x * 8.93 * 10^4) = 1.0119*e^(-1.08)
You asked:
Investigate the equation: \({e}^{-x \cdot 8.93 \cdot {10}^{4}} = 1.0119 {e}^{-1.08}\).
MathBot Answer:
The real solution is: \[x = - \frac{\log{\left(\frac{10119}{10000 e^{\frac{27}{25}}} \right)}}{89300} \approx 1.1961593 \cdot 10^{-5}\]
The complex solutions are: \[\left\{\frac{n i \pi}{44650} - \frac{\log{\left(\frac{10119}{10000 e^{\frac{27}{25}}} \right)}}{89300}\; \middle|\; n \in \mathbb{Z}\right\}\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).
\(i\) is the imaginary unit, defined as \(i^2 = -1\).