# Mathematical Fundamentals - PowerPoint PPT Presentation

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## Mathematical Fundamentals

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### Mathematical Fundamentals. Properties of Logarithms: 1. Logb is strictly increasing ... Logb ba = a (Logb b = 1) Properties of Logarithms: 2. Logb (xy) = Logb x ... – PowerPoint PPT presentation

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Title: Mathematical Fundamentals

1
Mathematical Fundamentals
2
Properties of Logarithms 1
• Logb is strictly increasing
• If xlty then logb x lt logb y
• Logb is one-to-one
• if logb x logb y then x y
• Logb 1 0
• Logb ba a (Logb b 1)

3
Properties of Logarithms 2
• Logb (xy) Logb x Logb y
• Logb xa a Logb x
• xLogb y yLogb x
• Loga x (Logb x)/(Logb a)

4
Probability
• X(x1, x2, ... , xn) X is a set of numbers
• P(p1, p2, ... , pn) P is a set of
probabilities
• For all 1 i n, pn is the probability of xn
• Average x1p1x2p2 ... xnpn
• Usually written

5
Summations
6
Induction Basis Step
7
Induction Inductive Step
8
Integral Formulas
a-1
a
b
b1