logging in or signing up The Logarithm Laws manpreet.oberoi2 Download Post to : URL : Related Presentations : Let's Connect Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 772 Category: Education License: All Rights Reserved Like it (2) Dislike it (0) Added: May 25, 2010 This Presentation is Public Favorites: 1 Presentation Description No description available. Comments Posting comment... By: allan4k4 (41 month(s) ago) nice presentation....it is very useful for childrens... Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript The Logarithm Laws : The Logarithm Laws Slide 2: Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the same as the rules for exponents. Slide 3: Exponents Logarithms bm × bn = bm+n logb xy = logb x + logb y bm ÷ bn = bm-n logb (x/y) = logb x − logb y (bm)n = bmn logb (xn) = n logb x b1 = b logb (b) = 1 b0 = 1 logb (1) = 0 Slide 4: Note: On our calculators, "log" (without any base) is taken to mean "log base 10". So, for example "log 7" means "log107". 1. Expand log 7x as the sum of 2 logarithms. : 1. Expand log 7x as the sum of 2 logarithms. Sol: Using the first law given above, our answer is log 7x = log 7 + log x Note: This has the same meaning as 107 × 10x = 107+ x 2. Using your calculator, show thatlog (20/5) = log 20 − log 5. : 2. Using your calculator, show thatlog (20/5) = log 20 − log 5. using numbers this time so you can convince yourself that the log law works. LHS = log (20/5) = log 4 = 0.60206 (using calculator) Now, Slide 7: RHS = log 20 − log 5 = 1.30103 − 0.69897 (using calculator) = 0.60206 = LHS We have shown that the second logaritm law above works for our number example. 3. Express as a multiple of logarithms: log x5. : 3. Express as a multiple of logarithms: log x5. Using the third logarithm law, we have log x5 = 5 log x We have expressed it as a multiple of logarithm, and it no longer involves an exponent. Slide 9: Note 1: Each of the following is equal to 1: log6 6 = log10 10 = logx x = loga a = 1 The equivalent statements, using ordinary exponents, are as follows: 61 = 6 101 = 10 x1 = x a1 = a Slide 10: Note 2: All of these are equivalent to 0: log7 1 = log10 1 = loge1 = logx 1 = 0 The equivalent statments in exponential form are: 70 = 1 100 = 1 e0 = 1 x0 = 1 THANK YOU : THANK YOU You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.