chapter 4

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Author:
Anonymous
ID:
259854
Filename:
chapter 4
Updated:
2014-02-02 17:48:41
Tags:
math transcendental functions
Folders:
Ma105 Theories
Description:
Theses are the theories for chapter 4 that you'll need to know in class Monday...And you'll need to prove one of the log properties (your choice of which one).
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  1. DEFINE:
    one-to-one function
    f(a) = f(b) only when a = b.
  2. DEFINE:
    Inverse Function
    If the ordered pairs of a function g are the ordered pairs of a function f w/ the order of the coordinates reversed, then the g is the inverse function of f.
  3. DEFINE:
    Exponential Function
    • The exponential function w base b is defined by
    • f(x)= bx
    • where b>0, b!=1, and x is a real number.
  4. DEFINE:
    Logarithmic Function
    • If x>0 and b is a positive constant except for 1 (b!=1), then y=logbx iff by=x.
    • ******
    • 1. logbb = 1
    • 2. logb1 = 0
    • 3. logbb= x
    • 4. blogb= x
  5. LAWS OF LOG.s:
    1. Product Property
    logbM*N = logbM + logbN
  6. LAWS OF LOG.s:
    2. Quotient Property
    logb(M/N) = logbM - logbN
  7. LAWS OF LOG.s:
    3. Power Property
    the logbM= P*logbM
  8. LAWS OF LOG.s:
    4. Change of Base Property
    • If x, a, and b are positive real numbers w/ a != 1 and b != 1, then
    • logbx = logax
    •             logbb

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