1 / 11

8.5 Properties of logarithms

This comprehensive overview covers crucial properties of logarithms, including the Product, Quotient, and Power properties. Practical examples demonstrate how to expand and condense logarithmic expressions effectively. By utilizing approximate logarithmic values for log 5 and log 7, learners can practice calculations involving logarithmic expressions and hone their skills in applying these properties in various contexts. Includes assignments to reinforce learning. Perfect for students seeking to master logarithm concepts!

aimon
Télécharger la présentation

8.5 Properties of 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. 8.5Properties of logarithms p. 493

  2. Properties of Logarithms • Let b, u, and v be positive numbers such that b≠1. • Product property: • logbuv = logbu + logbv • Quotient property: • logbu/v = logbu– logbv • Power property: • logbun = n logbu

  3. Use log53≈.683 and log57≈1.209 • Approximate: • log53/7 = • log53 – log57 ≈ • .683 – 1.209 = • -.526 • log521 = • log5(3·7)= • log53 + log57≈ • .683 + 1.209 = • 1.892

  4. Use log53≈.683 and log57≈1.209 • Approximate: • log549 = • log572 = • 2 log57 ≈ • 2(1.209)= • 2.418

  5. Expanding Logarithms • You can use the properties to expand logarithms. • log2 = • log27x3 - log2y = • log27 + log2x3 – log2y = • log27 + 3·log2x – log2y

  6. Your turn! • Expand: • log 5mn= • log 5 + logm + logn • Expand: • log58x3 = • log58 + 3·log5x

  7. Condensing Logarithms • log 6 + 2 log2 – log 3 = • log 6 + log 22 – log 3 = • log (6·22) – log 3 = • log = • log 8

  8. Your turn again! • Condense: • log57 + 3·log5t = • log57t3 • Condense: • 3log2x – (log24 + log2y)= • log2

  9. Change of base formula: • u, b, and c are positive numbers with b≠1 and c≠1. Then: • logcu = • logcu = (base 10) • logcu = (base e)

  10. Examples: • Use the change of base to evaluate: • log37 = • (base 10) • log 7 ≈ • log 3 • 1.771 • (base e) • ln 7≈ • ln 3 • 1.771

  11. Assignmentpg. 49615 – 72 x 3’s and80-85 all

More Related