Logarithmic Functions Objectives: Students will be able to… Convert between exponential and logarithmic equations Evaluate logarithmic equations Graphing logarithmic functions Domain of logarithmic equations Solving logarithmic equations Copyright © 2013 Pearson Education, Inc. All rights reserved
Essential Questions How are exponential and logarithmic functions related? How do you convert logarithmic functions to exponential functions? Exponential to logarithmic? Copyright © 2013 Pearson Education, Inc. All rights reserved
Logarithmic Functions Shortcuts log10 x = log x (Common log) loge x = ln x (Natural log) where e = 2.71828... (Euler’s number – irrational) logb1 = 0 (because b0 = 1) logbb = 1 (because b1 = b) logbbr = r (because br = br) blog b M = M (because logbM = logbM) Simpify. 1. 2.
Base Solution Exponent Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
logBASEANSWER=EXPONENT Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Converting BASEEXPONENT = ANSWER 42 = 16 4 is the base. 2 is the exponent. 16 is the answer. logBASEANSWER=EXPONENT log 4 16 = 2
b = ln 9 Copyright © 2013 Pearson Education, Inc. All rights reserved
ln b = - 3 ln b = - 3 Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Evaluating Logarithmic Functions Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Evaluating Logarithmic Functions 1. log105 2. 3. log35 4. Base other than 10 Calculator: Math > logBASE()
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Graphing Logarithmic Functions Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Graphing Logarithmic Functions 1) y = log x 2) y = 2log (x+3) – 2 3)
Properties of Logarithms Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Properties of Logarithms logbM + logbN = logb(MN) Ex: log4(5·3) logbM – logbN = logb(M/N) Ex: log3(50/2) r logbM = logbMr Ex: log7 x3 logbM-1 = logb(1/M) Ex: log11 (1/8)
Simplify log 7 + log 4 – log 2 = Simplify ln e2 = Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Worktime Simplify log 7 + log 4 – log 2 = Simplify ln e2 = Simplify e 4ln(3) - 3ln(4) = Expand log = Expand ln (abc) =
Simplify log 7 + log 4 – log 2 = Simplify ln e2 = Objective: Students will be able to convert between logarithmic and exponential functions CCSS: F-BF.4 Inverse functions, F-LE.4 Logarithmic functions Essential Question: What strategies do you use to solve logarithmic equations? Worktime Simplify log 7 + log 4 – log 2 = Simplify ln e2 = Simplify e 4ln(3) - 3ln(4) = Expand log = Expand ln (abc) =
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Inequality Set Notation Objective: Students will be able to convert quadratic equations. CCSS: A-REI.4 Re-write quadratic equations Essential Question: What information does each form of a quadratic equation give you? Words Inequality Set Notation Interval Notation All real numbers All real numbers less than 4 All real numbers less than or equal to 4 All real numbers greater than - 2 All real numbers greater than or equal to - 2 All real numbers greater than 0 and less than 5 All real numbers greater than or equal to 0 and less than or equal to 5 All real numbers greater than or equal to - 6 and less than 5 All real numbers greater than -6 and less than or equal to 5
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved