1 / 8

10-4 Common logarithms

10-4 Common logarithms. What you ’ ll learn. Solve exponential equations and inequalities using common logarithms Evaluate logarithmic expressions using the Change of Base Formula. Key words. Common logarithms : logarithms that use 10 as the base

Download Presentation

10-4 Common 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. 10-4 Common logarithms

  2. What you’ll learn • Solve exponential equations and inequalities using common logarithms • Evaluate logarithmic expressions using the Change of Base Formula

  3. Key words • Common logarithms : logarithms that use 10 as the base • Change of Base Formula : allows you to write equivalent logarithmic expressions that have different bases.

  4. Common logarithms • Common logarithms are usually written without the subscript 10 Ex) log10 x = log x, x > 0

  5. Change of Base Formula • For all positive numbers, a, b and n, where a and b doesn’t equal to 1, • log a n = log b n / log b a Ex) log5 = log10 12 / log 10 5

  6. Change of Base Formula example • Express log4 25 in terms of common logarithms. Then approximate its value to four decimal places. Log4 25= log10 25 / log10 4 ≈ 2.3219

  7. Proving the formula • To prove the change of base formula, let log a n = x, ax = n Log b ax = log b n x log b a = log b n x = log b n / log b a Log a n = log b n / log b a

  8. Solving Exponential Equations • Solve 3x = 11 3x = 11 Log 3x = log 11 x log 3 = log 11 x = log 11 / log 3 x ≈ 1.0414 / 0.4771 x ≈ 2.1828

More Related