chapter 4 theories

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Author:
jlane799
ID:
259863
Filename:
chapter 4 theories
Updated:
2014-02-02 19:49:29
Tags:
functions math theories logarithms
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Ma105 Transcendental Functions
Description:
math function theories to know for Monday's test
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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 g is the inverse function of f.
  3. DEFINE:
    Exponential Function
    The exponential function w/ base b is defined by f(x)=bwhere > 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
    • ************
    • let logbM = x and logbN = y,
    • then bx = M and by = N.
    • bx * by = M*N (multiplication prop.)
    • bx+y = MN (product law of exponents)
    • logbMN = x + y (substit. from the beginning)
    • logbMN = logbM + logbN (substit.)
  6. LAWS OF LOG.s:
    2. Quotient Property
    logb(M/N) = logbM - logbN
  7. LAWS OF LOG.s:
    3. Power Property
    • logbMP = P * logbM
    • ************
    • let logbM = x
    • then bx = M
    • (bx)P= MP
    • bx*P = MP
    • logbMP = xP
    • logbMP = P(logbM) (substit.)
  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
    •              logab
    • ************
    • logbx = y --> b= x
    • logaby = logax
    • ylogab = logax
    • y = logax 
    •       logab
    • logbx = logax 
    •              logab

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