1 / 13

7.4 Properties of Logarithms

7.4 Properties of Logarithms. Review: Properties of Exponents . 3 2 * 3 7. Product Property. The logarithm of a product is equal to the sum of the logarithms of the factors. Example: log 3 729 = log 3 (27 * 27) = log 3 27 + log 3 27 log b mn = log b m + log b n.

tobias-duncan
Download Presentation

7.4 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. 7.4 Properties of Logarithms

  2. Review: Properties of Exponents • 32 * 37

  3. Product Property • The logarithm of a product is equal to the sum of the logarithms of the factors. • Example: log3 729 = log3(27 * 27) = log3 27 + log3 27 • logbmn = logbm + logbn

  4. Quotient Property of Logarithms • The logarithm of a quotient is the logarithm of the dividend minus the logarithm of the divisor • log4 (16 ÷ 2) = log4 16 – log42 • logb(m÷n) = logbm – logbn

  5. Power property of Logarithms • Let’s try this one: log 103 (use the product property. • logbap = plogb a

  6. Inverse Property of Logarithms • How do you solve something like 2x – 5 = 9? • Use inverse operations. • So, how do you “undo” a log? An exponential? • logbbx = xblogbx=x

  7. Some problems • Simplify: log 100.9 • 2log2(8x) • log883x+1

  8. Change of Base Formula

  9. Express as a single logarithm. Simplify, if possible. • log550 + log5 62.5 • log 100 + log 1000 • log3 3 + log327

  10. Simplify and evaluate • log4320 – log45 • log 5.4 – log 0.054 • log6496.8 – log62.3

  11. Simplify • log882 • log335 • log7493 • log1/2(0.25)4

  12. Simplify • log22x+5 • 2.5log2.519 • log41024 • log2(0.5)4

  13. Evaluate • log9(1/27) • log832 • log510 • log227

More Related