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2-3 - 2-3 Logarithmic Functions The common log of a number...

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2-3 Logarithmic Functions The common log of a number is that exponent (or power) to which 10 must be raised to obtain the number. Notation :y = log (x) or y = log x "y = log of x" Example: log (1000) = . . . . . . the power to which 10 must be raised to obtain 1000 so log(1000) = 3 Another way to put it: 3 = log(1000) because 10 3 = 1000 y = log(x) means 10 y = x Be CAREFUL! log x + 2 log(x + 2) log x + 2 = log(x) + 2 Keep this in mind at all times: A LOG IS AN E XPONENT !!!! Practice: x 1 10 1000 .1 log x 2-3 p. 1
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Since logs are defined using exponentials, any “log x” has an equivalent “exponent” form, and vice-versa. Going from log form to exponent form (a visual scheme) LOG FORM EXPONENT FORM Ex. log 5 13 = x 5 x = 13 Remember – a log is an exponent ___________________________________________ Going from exponent form to log form EXPONENT FORM LOG FORM Ex. y 14 = x ==> log y x = 14 Remember -- a log is an exponent 2-3 p. 2
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Inverse properties of logarithms Think about log 10 x : log 10 x is the power to which we must raise 10 to get 10 x which is … x! so … log 10 x = x Think about … 10 log x : log x
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