1. QUIZ 3.1 Exponential Functions and Inverse Trig

2. Check HW 3.2: Pg. 236 #2-16 even, 17-22 all, 31, 40-60even
34 = ln = 2
= 1/ ln = 1/3
163/4 = D: (0,∞); ln = -4.1
8. 82/3 = xint: (1, 0); ln 3 = 2x
log864 = Vert asymp x = 0
12. log927 = 3/ f
14. log41/64 = e
log = a
e-0.916… = 2/5
1/ e2.302… = 10
e6.520… = 679
e1 = e

3. 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

4. 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

5. 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

6. 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)

7. 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

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

9. 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