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Why is $ce^λ=1$ equal to $c=e^{-λ}$?

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closed as off-topic by Brahadeesh, Adrian Keister, Haris Gusic, Jean-Claude Arbaut, steven gregory Apr 17 at 21:23

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$\frac {1}{e^x} $ can be written as $e^{-x}$ because it is the law of indices. Moreover $1$ when multiplied by any number will result in the same number

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If you multiply both sides of the equation by $e^{-\lambda}$ you obtain:

$$ce^{\lambda}e^{-\lambda}=e^{-\lambda}$$

We have $a^xa^y=a^{x+y}$, so $$e^{\lambda}e^{-\lambda}=e^{\lambda-\lambda}=e^0=1$$ therefore: $$c=e^{-\lambda}$$

You can analogically show it the other way (from $c=e^{-\lambda}$ to $ce^{\lambda}=1$) by multiplying both sides by $e^{\lambda}$

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