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DEFINE:
Onetoone Function
f(a) = f(b) only when a = b.

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.

DEFINE:
Exponential Function
The exponential function w/ base b is defined by f(x)=b^{x }where b > 0, b != 1, and x is a real number

DEFINE:
Logarithmic Function
 If x>0 and b is a positive constant except for 1 (b!=1), then y=log_{b}x iff b^{y}=x.
 ***********
 1. log_{b}b = 1
 2. log_{b}1 = 0
 3. log_{b}b^{x }= x
 4. b^{logbx }= x

LAWS OF LOG.s:
1. Product Property
 log_{b}M*N = log_{b}M + log_{b}N
 ************
 let log_{b}M = x and log_{b}N = y,
 then b^{x} = M and b^{y} = N.
 b^{x} * b^{y} = M*N (multiplication prop.)
 b^{x+y} = MN (product law of exponents)
 log_{b}MN = x + y (substit. from the beginning)
 log_{b}MN = log_{b}M + log_{b}N (substit.)

LAWS OF LOG.s:
2. Quotient Property
log_{b}(M/N) = log_{b}M  log_{b}N

LAWS OF LOG.s:
3. Power Property
 log_{b}M^{P} = P * log_{b}M
 ************
 let log_{b}M = x
 then b^{x} = M
 (b^{x})^{P}= M^{P}
 b^{x*P} = M^{P}
 log_{b}MP = xP
 log_{b}MP = P(log_{b}M) (substit.)

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
 log_{b}x = log_{a}x
 log_{a}b
 ************
 log_{b}x = y > b^{y }= x
 log_{a}b^{y} = log_{a}x
 ylog_{a}b = log_{a}x
 y = log_{a}x
 log_{a}b
 log_{b}x = log_{a}x
 log_{a}b

