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Lecture 2 - Logarithms

Lecture 2 - Logarithms - of 5000 is only 0.69897 bigger...

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bx=y x = log b (y) Logarithms A logarithm is a way of expressing numbers as functions of a common base. In mathematical symbols: b = the base x = the exponent y = the number bx
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bx=y x = log b (y) Logarithms How do we use logarithms? log 10 (100) = ? this statement is asking: to what power do you raise the number 10 to get the number 100? or: 10 ? = 100 The “?” is the answer, or the log. In this case, 102=100 so log 10 (100) = 2
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log 10 (10) = ? log 10 (100) = ? log 10 (1000) = ? log 10 (5000) = ? ? = 1 ? = 2 ? = 3 ? = 3.69897 10 ? = 10 10 ? = 100 10 ? = 1000 10 ? = 5000 Logarithms Try to complete these without a calculator (estimate where necessary). Click through for answers: 10, 100, 1000 are what we commonly refer to as orders of magnitude. Each number is a power of 10 larger than the previous, and the base 10 logarithm of these numbers reflects that. Notice that 5000 is much larger (5 times!) than 1000, but the log base 10
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Unformatted text preview: of 5000 is only 0.69897 bigger than the log base 10 of 1000. This is because 5000 is not an order of magnitude, or power of 10, larger than 1000. The log 10 of 5000 has to be between 3 and 4 (because the number 5000 is between 103 and 104) Logarithms The Log Scale 1 10 6 10 5 10 3 10 4 10 1 10 2 20 30 40 10 2 3 4 200 300 400 2000 3000 4000 0 1 2 3 4 5 6 7 8 9 10 Graph these points: (7, 10) (3, 6) (6, 20000) (5, 300000) Logarithms The Log Scale 1 10 6 10 5 10 3 10 4 10 1 10 2 20 30 40 10 2 3 4 200 300 400 2000 3000 4000 0 1 2 3 4 5 6 7 8 9 10 Graph these points: (7, 10) (3, 6) (6, 20000) (5, 300000) Logarithms Logs in bases other than 10 work the same way as logs of base 10: Log 2 (4) = ? 2?=4 ?=2 Log 2 (16) = ? 2?=16 ?=4 Log 2 (25) = ? 2?=25 ?=4.64...
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