1 / 8

Introduction to Logarithms

Introduction to Logarithms. Chapter 8.4. Logarithmic Functions. log b y = x if and only if b x = y. Logarithmic Form log 2 32 = 5. Exponential Form 2 5 = 32. ( ) -1 = 2. 1 2. Rewriting Logarithmic Equations. log 5 1 = 0. 5 0 = 1. log 10 10 = 1. 10 1 = 10.

kaden
Download Presentation

Introduction to Logarithms

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. Introduction to Logarithms Chapter 8.4

  2. Logarithmic Functions logby = x if and only if bx = y

  3. Logarithmic Form log232 = 5 Exponential Form 25 = 32 • ( )-1 = 2 1 2 Rewriting Logarithmic Equations • log51 = 0 • 50 = 1 • log1010 = 1 • 101 = 10 • log½2 = -1

  4. Special Logarithmic Values • Logarithm of 1 logb1 = 0 because b0 = 1 • Logarithm of Base b logbb = 1 because b1 = b

  5. Evaluating Logarithmic Expressions • Evaluate log381 3 to what power gives 81? 34 = 81, therefore log381 = 4

  6. The Common Logarithm • The logarithm with base 10 is called the common logarithm. • It is denoted log10 or simply log. • The log button on your calculator evaluates common logarithms.

  7. logbu logbc log u logc Change of Base Formula • Let u, b, c be positive numbers b  1 and c  , logcu = • So to convert expressions to common logarithms in order to use your calculator • logcu =

  8. Properties of Logarithms Let b, u , and v be positive and b  1 • Product Property logbuv = logbu + logbv • Quotient Property logb = logbu – logbv • Power Property logbun = n logbu u v

More Related