1 / 10

Logarithms and Their Properties

Logarithms and Their Properties. Lesson 4.1. Recall the Exponential Function. General form Given the exponent what is the resulting y-value? Now we look at the inverse of this function Now we will ask, given the result, what exponent is needed to achieve it?. A New Function.

denisewilson
Download Presentation

Logarithms and Their Properties

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Logarithms and Their Properties Lesson 4.1

  2. Recall the Exponential Function • General form • Given the exponentwhat is the resulting y-value? • Now we look at the inverse of this function • Now we will ask, given the result, what exponent is needed to achieve it?

  3. A New Function • Consider the exponential function y = 10x • Based on that function, declare a new function x = log10y • You should be able to see that these are inverse functions • In general • The log of a numberis an exponent

  4. Note: if no base specified, default is base of 10 The Log Function • Try Theselog39 = ? log232 = ? log 0.01 = ?

  5. Properties of Logarithms • Note box on page 154 of text • Most used properties

  6. Natural Logarithms • We have used base of 10 for logs • Another commonly used base for logs is e • e is an irrational number (as is ) • e has other interesting properties • Later to be discovered in calculus • Use ln button on your calculator

  7. Properties of the Natural Logarithm • Recall that y = ln x  x = ey • Note that • ln 1 = 0 and ln e = 1 • ln (ex) = x (for all x) • e ln x = x (for x > 0) • As with other based logarithms

  8. Note this is not the same aslog 1.04 – log 3 Use Properties for Solving Exponential Equations • Given • Take log ofboth sides • Use exponent property • Solve for whatwas the exponent

  9. Misconceptions • log (a+b) NOT the same as log a + log b • log (a-b) NOT the same as log a – log b • log (a * b) NOT same as (log a)(log b) • log (a/b) NOT same as (log a)/(log b) • log (1/a) NOT same as 1/(log a)

  10. Assignment • Lesson 4.1 • Page 157 • Exercises 1 – 51 odd

More Related