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Warm Up 11/19Lesson 4-2: Logarithmic FunctionsObjectiveStudents will…Be able to define the logarithmic function, as the inverse of the exponential functionBe able to know and apply the properties of logarithmsBe able to use calculators to compute logarithmsInversesIn mathematics, inverses can be defined as the reverse operation (operations that revert the original operation). We’ve dealt with plenty of examples of inverses in the past. Consider the following examples. Starting with ?…Multiplication and division: Addition and subtraction: Powers and roots: One-to-one Function and Inverse Function: The Inverse of Exponential FunctionWith regards to the exponential function, there exists an inverse function which is called the Logarithmic Function.Definition: Let ? be a number with ?≠1. The logarithmic function with base ?, denoted by _______ is defined by if and only ifSo, here ? is the exponent to which the base ? must be raised to give ?.ExamplesRevisiting our warm-up problems then…1) 2x=82) 4x=163) 3x=27 ?=3 means ?=2 means ?=3 means4) 5x=6255) ex=16) 10x=100000 ?=4 means ?=0 means ?=5 meansProperties of LogarithmsWe are familiar with some of the properties of exponents. Here, we’ve established that ??????? is an exponent. Therefore, the properties of logarithms exist, much similar to the properties of exponents. PropertyReason1. Anything raised to the zero power is 12.Anything raised to the 1st power is itself3.? raised to the ? power is ?????4. _____________ is the power to which ? must be raised to get ?ExamplesFor base 5…By property 1:By property 2:By property 3:By property 4:You tryFor base 10…By property 1:log101=By property 2:log1010=By property 3:log10104=By property 4:10log1011=Common LogarithmIn logarithms, base 10 is considered the “standard base.” Therefore, it has a special name within the logarithmic mon Logarithm- Base 10 said to be the common base, so any log base 10 is denoted without the base written:log109=log?9So always assume that log has base 10 if there is no base written.Ex. log100=2 and log10=1In ClosingHomework 11/19TB pg. 349-350 #1, 3-5, 9, 12, 15, 19, 29 ................
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