1 / 14

Understanding Logarithms and their Properties: Calculation and Equation Solving

This comprehensive guide delves into logarithms and their properties, detailing how to convert between logarithmic and exponential forms. It provides step-by-step instructions for solving logarithmic equations using a calculator and offers challenges without a calculator to deepen understanding. Additionally, it explains the change of base formula for evaluating logarithms with diverse bases. Featuring various examples and solutions, this resource is perfect for students seeking to enhance their skills in logarithmic calculations and applications.

nitsa
Télécharger la présentation

Understanding Logarithms and their Properties: Calculation and Equation Solving

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… Exponential form Change of Base Properties

  2. Use your calculator to solve the following • 10x = 32 x = _____ • 10x = 50 x = _____ • 10x = 207 x = _____ • 10x = 2 x = _____

  3. Using the Log key on your calculator find each of the following • Log 32= _____ • Log 50= _____ • Log 207 = ____ • Log 2 = _____

  4. NO CALCULATOR • If 101.681 = 48, what is log 48 ? _____ • If log 156 = 2.193, what is 102.193 ? __ • Log(103) = ___ • 10log 100 = ____

  5. Use your calculator to solve the following • 2x = 32 x = ____ • 2x = 50 x = ____ • 2x = ¼ x = ____ • Log2 ¼ = ___ • Log250 = ___ • Log232 = ___

  6. General Form • Logarithmic form • Logba = c • Exponential form • bc = a

  7. No Calculator Log864 = ____ Log464 = ____ Log264 = ____ Log6464 = ____ Log81 = ____ Log8 (1/64) = ____

  8. No Calculator • If 52.892 = 105, then log5105 = ____ • If log217 = 4.088, what is 24.088 ? • log5(54) = ____ • = ____

  9. Natural Log (ln) is a special log with a base e. • Basic Log Properties: • ln 1 and log 1 = 0 • lne = 1 • logbb = 1 • elnx = x • blogbx = x

  10. Rules for Logs

  11. Examples: Use the properties of logs to expand. Write as a single log:

  12. Change of Base • Since our calculators can only evaluate a base of 10 or e, we will let a = 10 or use ln. • This formula allows us to evaluate logs with ANY base using the calculator!

  13. Examples Evaluate using change of base:

More Related