There are a number of rules which enable us to rewrite expressions involving log
ID: 3614192 • Letter: T
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There are a number of rules which enable us to rewrite expressions involving logarithms in different, yet equivalent, ways. These rules are known as the laws of logarithms. The laws apply to logarithms of any base but the same base must be used throughout a calculation. logA + logB = logAB This law tells us how to add two logarithms together. Adding log A and logB results in the logarithm of the product of A and B. which is log AB e.g.. we can write log2 8 + log2 5 = log2(8 X 5) = log2 40 The same base, in this case 2. is used throughout the calculation. You should verify this by evaluating both sides separately on your calculator. Different base logarithms cannot be added. log A - log B = log A/B So, subtracting log B from log A results in logA/B For example, we can write log2 12 - log2 4 = log2 12/3 = log2 4 The same base, in tins case e. is used throughout the calculation. You should verify this by evaluating both sides separately on your calculator. logAz = n logA So, for example, log2 53 = 3 log2 5 You should verify this by evaluating both sides separately on your calculator. Base is not interchanged. Use the first law to simplify The following. log105 + log10 5 logx + logyz log25A + log2v log ox +log by + log c Use the second law to simplify the following. log10100-log1010 log20-log10 log5000-log100 log 5-log 5000 Use the third law to write each of the following in an alternative form. 21og22 3 logx log(5x)2 Compare the growth of the following functions using "0", "omega" and "Theta" notations. For example 50 = O(lg n), you do not need to justify your answers. 7n and 1000n n and n/2 1/n[n3] and 1/n3[n4] Hint: n2 = O(n3)Explanation / Answer
Question 1: 1. log10(25) 2. log(xyz) 3. log (50xy) 4. log(abcxy) Question 2: 1. log10(100/10) = log1010 2.log 2 3.log 50 4.log(0.001) Question 3: 1. log2 22 2. log 3x 3. 2 log (5x) Question 4: Will have to be answered by someone else, as I don't have thetime. Sorry.
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