Laws of Exponents: e^(x+y) = e^x·e^y

[mes]

In this video I go over laws of exponents and prove that e^(x+y) = e^x·e^y. In this prove I first consider the natural logarithm function, ln(x), and use log properties and laws to simplify and breakdown the function in proofing the exponent law.

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Laws of Exponents: e^x+y = e^xe^y

If x and y are real numbers and r is rational, then:

1. e^x+y = e^xe^y
2. e^x-y = e^x/e^y
3. (e^x)^r = e^{r x}

Proof:

Ln is a one-to-one function: meaning that each y-value has exactly one x-value.