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.) 3x = 27 2.) log4 + log39 3.) 25x+2 =125 4.) lnex + 4 = 2 5.) log1000 + log232

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

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

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

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

10 x = 35 2x = 3 log1010x = log1035 log22x = log23

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