# Why is $ce^λ=1$ equal to $c=e^{-λ}$? [closed]

Why is $$ce^λ=1$$ equal to $$c=e^{-λ}$$?

## closed as off-topic by Brahadeesh, Adrian Keister, Haris Gušić, Jean-Claude Arbaut, steven gregoryApr 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
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 $$e^{\lambda}$$