Chapter 6 - Inverse Functions - 6.3* The Natural Exponential Function - 6.3* Exercises: 107

$b^{x-y}=\frac{b^{x}}{b^{y}}$; Second Law of Exponents

Work Step by Step

We already know that $b^{x}=e^{xlnb}$ Now, $b^{x-y}=e^{(x-y)lnb}$ This implies $b^{x-y}=e^{xlnb-ylnb}=\frac{e^{xlnb}}{e^{ylnb}}$ Hence, $b^{x-y}=\frac{b^{x}}{b^{y}}$ This is known as second Law of Exponents; where x and y are real numbers.

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