Logarithmic Functions

Inverses of Exponentials

Let's start by thinking about some real-life problems that would require the use of the inverse of an exponential function.
- From science:
  - "How much uranium-235 will I have after one hundred years, if I start with a kilogram?"
  - "What's the difference in energy between an earthquake of 8 and an earthquake of 9 on the Richter scale?"
- From business: "How long will it take my money to double at 5 percent interest, compounded continuously?"
Definition:
Logarithms are, by definition, the inverses of the exponential functions:
The laws of logarithms are reflections of the properties of exponentials:
The most important exponential is base e, and so the most important inverse is its inverse:
Another important base is base 10: if we write simply ${\log}$ , we generally mean ${\log_{10}}$ . You may well have special keys on your calculator for both ${ln}$ and ${\log}$ .
Examples:
- #4, p. 322
- #10
- #15
- #23
- #31
- #47
- #88

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