mac1105_lecture23_1

mac1105_lecture23_1 - L23 Logarithmic Functions;...

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249 L23 Logarithmic Functions; Applications of Logarithms The exponential function () x fx a = (0 , 1 ) aa >≠ is a one-to-one function. Thus, its inverse is also a function. We call the inverse the logarithmic function to the base a and denote 1 log a fx x = . The general property of the inverses ( ) 1 y f y x = ⇔= , when applied to logarithms and exponents, has a form x ay = log a yx = Also, Domain log a x = Range ( ) x a = 0, +∞ Range log a x = Domain ( ) x a = , −∞ +∞ The Cancellation Rules for logarithms and exponents : log for all real x a ax x = log for 0 a x x = >
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250 We can use the cancellation rules when converting from the logarithmic form to the equivalent exponential form or vice versa: When converting from the logarithmic form log a x y = to the exponential form y x a = , we compose the exponential function with the base a to both sides and simplify: When converting from the exponential form x ay = to the logarithmic form log a x y = , we compose logarithmic function with the base a to both sides and simplify:
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251 Example
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This note was uploaded on 11/07/2011 for the course MAC 1105 taught by Professor Picklesimer during the Fall '10 term at University of Florida.

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mac1105_lecture23_1 - L23 Logarithmic Functions;...

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