124 Logarithmic Functions Objectives Students will be able
1/24 Logarithmic Functions Objectives: Students will be able to… - Convert between exponential and logarithmic equations - Evaluate logarithmic equations - Find the 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 log 10 x = log x (Common log) • loge x = ln x (Natural log) where e = 2. 71828. . . (Euler’s number – irrational) • logb 1 = 0 (because b 0 = 1) • logbb = 1 (because b 1 = b) • logbbr = r (because br = br) • blog b M = M (because logb. M = logb. M) Simpify. 1. 2.
Base Solution Exponent Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
Converting BASEEXPONENT = ANSWER 42 = 16 • 4 is the base. 2 is the exponent. 16 is the answer. • log. BASEANSWER=EXPONENT • log 4 16 = 2
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ln b = - 3 Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
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. log 105 2. Base other than 10 3. log 35 4. Calculator: Math > log. BASE()
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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 = 2 log (x+3) – 2 3)
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 • logb. M + logb. N = logb(MN) Ex: log 4(5· 3) • logb. M – logb. N = logb(M/N) Ex: log 3(50/2) • r logb. M = logb. Mr Ex: log 7 x 3 • logb. M-1 = logb(1/M) Ex: log 11 (1/8)
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 1. Simplify log 7 + log 4 – log 2 = 2. Simplify ln e 2 = 3. Simplify e 4 ln(3) - 3 ln(4) = 4. Expand log 5. Expand ln = =
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 1. Simplify log 7 + log 4 – log 2 = 2. Simplify ln e 2 = 3. Simplify e 4 ln(3) - 3 ln(4) = 4. Expand log 5. Expand ln (abc) = =
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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 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 Inequality Set Notation Interval Notation
Copyright © 2013 Pearson Education, Inc. All rights reserved
Copyright © 2013 Pearson Education, Inc. All rights reserved
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