# Questions tagged [exponential-function]

For question involving exponential functions and questions on exponential growth or decay.

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### Error propagation on a 5 order polynomial

I have a 5 order polynomial equation which gives log of a chi factor required to convert equivalent widths to normalised H alpha luminosity for M dwarfs, (Reiners et al. 2008). I would like to get the ...
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### Could someone explain the the steps mention in the description? [closed]

Why$$\ln|y| = \ln|1+x| + c$$ can be written as $$y = e^{\ln|1+x| + c}$$ Also, why $$e^{\ln|1+x|} = 1+x$$
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### How to simplify sum of exponential functions

I have been having some issues with simplifying the following equation: $p\Big[ \frac{e^{ay}+e^{a(10+y)}}{e^{a(10-y)}+e^{a(20-y)}} \Big]=1-p$ where $y$ is the variable, $a$ is a parameter and $p$ is a ...
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### Problem manually evaluating definite integral

I seem to be quite stuck when trying to normalize a probability density given as $$p(x|\omega_i)\propto e^{-\frac{|x-a_i|}{b_i}}$$ with $a_i\in R$ and $b_i\in R^+$. Although I was able to "...
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### Expansion of $e^x$ - correct form

I have come across in a textbook to an expansion of e to the x in the following form: $$1+ \frac1x + \frac1{x^2} + \frac1{x^3} + \ldots$$ Is the above correct or is it a typo? I am familiar with ...