QUIZ 3.1 Exponential Functions and Inverse Trig

Check HW 3.2: Pg. 236 #2-16 even, 17-22 all, 31, 40-60even 34 = 81 21. 2 54. ln 7.3890 = 2 4. 10-3 = 1/1000 22. -3 56. ln 1.3956 = 1/3 163/4 = 8 31. D: (0,∞); 58. ln 0.0165 = -4.1 8. 82/3 = 4 xint: (1, 0); 60. ln 3 = 2x log864 = 2 Vert asymp x = 0 12. log927 = 3/2 40. f 14. log41/64 = -3 42. e log 0.001 = -3 44. a 17. 4 46. e-0.916… = 2/5 1/2 48. e2.302… = 10 0 50. e6.520… = 679 1 52. e1 = e

February 14, 2012 At the end of today, you will be able to use log properties to simplify. Valentine’s Warm-up: Draw a heart on your graphing calculator. Give me the equations you typed in and show your work to get full credit. *Hint: Solve for Y HW 3.3a: Pg. 237 #79-85odd, Pg. 243 #39-72 mult of 3

Properties of Exponents When you multiply two terms with the same base, you ADD the exponents. x3  x4 = When you divide two terms with the same base, you SUBTRACT the exponents. When you have a power to a power, you MULTIPLY the exponents. x7 x4 x12

Lesson 3.3 Properties of Logs loga 1 = 0 loga a = 1 loga ax = x and If loga x = loga y, then x = y (One-to-one Property) log33 = 1 log332 = 2 5 log2 3 = log2 2y 2y = 3 y = 3/2

Example 1: Using the One-to-One Property to solve 1. log3(7x – 6) = log3(4x + 9) 2. log11(3x – 24) = log11(-5x – 8) 3. log12(x2 – 7) = log12(x + 5)

More Properties of Logarithms Let b be a positive number such that b ≠ 1, and let n be a real number. If u and v are positive real numbers, the following properties are true. Product Property: logb(uv) = logbu + logbv ln(uv) = ln u + ln v Quotient Property: Power Property: logbun = nlogbu ln un = nln u

Example 2: Using Log Properties to expand an expression log410x b) c) log4x5 d) e) ln abc3 f) log4 10 + log4 x log4 x – log4 10 5log4 x ln a + ln b + 3ln c -2log4 x

Example 3: Use the log properties to condense the expression to the log of a single quantity. Go the other way! ln x + ln 3 b) log4 z – log4 x c) 2log3 x + log3 y d) ln 3x log3 x2y