What is the Exponential Property Involving Products?

1 Answer
vince
Feb 18, 2015

Hello !

The exponential function x \mapsto e^xx↦ex has a fundamental property involving products :

\forall x,y \in \mathbb{R}, \quad e^{x+y} = e^x \times e^y.

So, exponential function transforms sums into products. Of course, you can write,

e^{x_1+x_2+\ldots + x_n} = e^{x_1}\times e^{x_1} \times \ldots \times e^{x_n}

for any numbers x_1,\ldots,x_n.

Note that there exists other exponential functions : x\mapsto 10^x, x\mapsto 2^x, ..., x\mapsto a^x for any positive real a. All of them have the same property involving products.

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