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Assignment, red pen, pencil, highlighter, textbook, GP notebook

total:. U6D7. Assignment, red pen, pencil, highlighter, textbook, GP notebook. Have out:. Bellwork:. Evaluate the following. 1). 2). 3). 4). 5). 3. 5. –2. –3. +1. +1. +1. +1. +1. Remember : With logarithms, we are looking for exponents.

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Assignment, red pen, pencil, highlighter, textbook, GP notebook

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  1. total: U6D7 Assignment, red pen, pencil, highlighter, textbook, GP notebook Have out: Bellwork: Evaluate the following. 1) 2) 3) 4) 5) 3 5 –2 –3 +1 +1 +1 +1 +1 Remember: With logarithms, we are looking for exponents. For example, #1 is read as: “4 to what power is 64?”

  2. Logarithms and Logarithmic Functions Definition of Logarithm For all positive real numbers x and b , b 1, the inverse of the exponential function y = bx is the logarithmic function ____________. x = log b y x = log b y y = bx In other words, ____________ if and only if ____________ When converting back and forth between exponential and logarithmic forms, be sure to identify the _____ and _________ first. base exponent exponent argument 72 = 49 log749 = 2 exponent argument base base

  3. I. Write each equation in logarithmic form. d) a) b) c) log 9 = 2 log 8 = 3 log = –2 3 2 8 log = 2 h) e) f) g) log 512 = 3 log 10 8 log = –2 16 log = –3 100 5

  4. 2. Write each equation in exponential form. a) b) c) 5 3 3 = 243 4 = 64 9 = 3 d) e) f) 2 13 = 169 –2 –1 5 4 g) h) 100 8 = 4

  5. I. Inverse Property of Exponents & Logs Evaluate each expression. = x = x = x = x d) a) b) c) 8 7 log log x x x x 6 = 6 3 = 3 4 5 What patterns do you notice? In parts (a) and (b), the answer is the “exponent.” In parts (c) and (d), the answer is the “argument.” If the bases of the exponential and the logarithmic forms are the _____, then the exponent and logarithm __________ each other. same “cancel out”

  6. 4. Evaluate each expression. d) a) b) c) 4 n – 5 45 3x + 2

  7. II. Solving Logarithmic Equations Some equations involving logarithms can be solved readily if they are first rewritten in exponential form. Steps: Example #1: log2(2x) = 3 exponent 1. Identify the base & exponent. log2(2x) = 3 2. Write in exponential form by using the definition of logarithms. base 3 2x = 2 2x = 8 3. Solve for x. 2 2 x = 4

  8. II. Solving Logarithmic Equations Some equations involving logarithms can be solved readily if they are first rewritten in exponential form. Example #2: log5(4x – 3) = 3 Steps: log5(4x – 3) = 3 1. Identify the base & exponent. exponent base 2. Write in exponential form by using the definition of logarithms. 3 4x – 3 = 5 4x – 3 = 125 +3 +3 3. Solve for x. 4x = 128 4 4 x = 32

  9. Finish today's assignment: Log Worksheet CC 74 – 76, 78, 79, 81

  10. Mixed Practice: Solve each equation. 1) log3x = 5 2) log2x = 3 10) log6(4x + 12) = 2 x = 35 x = 23 4x + 12 = 62 4x + 12 = 36 x = 243 x = 8 -12 -12 4x = 24 4 4 x = 6

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