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Understanding Logarithmic and Exponential Functions: A Quick Guide

Explore the fundamental concepts of logarithmic and exponential functions in this comprehensive guide. Learn about the challenges of solving these functions algebraically, discover the special notation for logarithms with base e, and understand the laws of logarithms. We'll also discuss how to use older calculators to handle these computations effectively and clarify the relationship between logarithmic and exponential functions as inverses of each other. Whether you're a student or just curious, this guide will enhance your mathematical skills.

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Understanding Logarithmic and Exponential Functions: A Quick Guide

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  1. Rules of Logarithmic and Exponential Functions 1

  2. Which of these would be hardest to solve algebraically? ? We do have a function that we can perform here that would actually help us solve for an unknown exponent.

  3. Logarithmic Functions By the way, the log with base e (loge ) has a special notation: Examples: Ex 1) Ex 2) a) b)

  4. Did You Know that this means this? We will find out why shortly

  5. Laws of Logs Really?  and therefore...

  6. Did You Know This?

  7. Ex 3 a)

  8. Only the most recent versions of the TI-84 have a log function with a variable base. But how would we do this on older calculators? How about using a log function that is on there like base 10? Change of Base Formula = 5

  9. These two equations say the same thing which tells us something: The log and exponential functions are inverses of each other This also tells us that algebraically, each can be used to “undo” the other What do I mean by this? Just watch… We can also do this This gives us these two expressions to remember and

  10. So let’s recap… And for the calculator… Which can be done using the two programmed bases More on this one soon…

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