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Ch. 3.3 Properties of Logarithms

Ch. 3.3 Properties of Logarithms. Objectives: 1.) To learn and practice using the change of base theorem 2 .) Solving exponentials with the change of base theorem. Warm-up Solve the equations and simplify the expressions. 1.) 3 x = 27 2.) log 4 + log 3 9

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Ch. 3.3 Properties of Logarithms

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  1. Ch. 3.3 Properties of Logarithms Objectives: 1.) To learn and practice using the change of base theorem 2.) Solving exponentials with the change of base theorem

  2. Warm-upSolve the equations and simplify the expressions 1.) 3x = 27 2.) log4 + log39 3.) 25x+2 =125 4.) lnex + 4 = 2 5.) log1000 + log232

  3. Vocabulary • Common logarithm/common log: A logarithm with base 10 • Natural logarithm/ natural log: A logarithm with base e

  4. Consider 3x = 27 Common Base Method 3x= 33 Common Base implies x = 3 Writing as a logarithm and using the change of base property log33x = log327 => x = log327

  5. Change of Base Theorem pg 219 The change of base theorem will allow you to take a logarithm with a certain base b, and write it as a quotient or ratio of logarithms of a different base. => x = log327

  6. What if I asked you to simplify 10 x = 35 2x = 3 log 35 or log23 What’s your problem? What?

  7. log1010x = log1035 log22x = log23 10 x = 35 2x = 3 x = log1035= x = log23 = ?

  8. Homework • Pg. 223 #1-3; 10-16(even; write the exponential equation you would be solving for); 76-80(even) Page 232 #2,5, 9-14; 24-28; 31-36; 46-50

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