Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3.3 Properties of Logarithms – Day 1 Goal(s): Use Change-of-Base property to rewrite and evaluate logarithms. Use properties of logarithms to expand logarithms into a sum, difference and/or multiple of logarithms. Lesson What is a good estimate of log 2 10 ? Change-of-Base Formula Let a, b, and x be positive real numbers such that a 1, and b 1 . Then log a x can be converted to a different base as follows. Base b log a x Ex 1. a) Ex 2. a) log b x log b a Base 10 log a x Base e log x log a log a x Write the logarithm as a ratio of common logarithms. b) Write the logarithm as a ratio of natural logarithms. b) ln x ln a Properties of Logarithms Let a be positive real number such that then the following properties are true. Product Rule EXAMPLE , and let n be a real number . If u and v are positive real numbers, Quotient Rule EXAMPLE Power Rule EXAMPLE Corresponding Properties of Exponents Product Rule Ex 3. Quotient Rule Power Rule Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.) Note: When more than one property is used do quotient 1st , product 2nd, and power 3rd . a) b) d) e) c) 3.3 Properties of Logarithms – Day 2 Goal(s): Use properties of logarithms to condense logarithmic expressions into a single logarithm. Ex 1. Condense the expression to the logarithm of a single quantity. Note: Apply power property 1st , then combine logarithms using product and quotient properties from left to right . a) b) d) e) c)