Introduction to Exponential Functions and Logarithm Functions

Introduction to Logarithmic Functions

A Logarithmic function with base b, where b > 0 and b is not equal to 1, is the inverse of the corresponding exponential function. These functions are useful in the study of computer algorithms and natural growth/decay phenomena of living beings, among other applications.

Learning Objectives:

  • Study and understand the basic logarithmic function \(f(x) = b^x\)
    • Domain, Range, Intercepts, Asymptote and Graph
  • Study and understand the basic logarithmic function \(a \cdot b^{mx + b} + d\) where \(b > 0, b\neq 1\)
    • Domain, Range, Intercepts, Asymptote and Graph
  • Learn and apply basic properties of logarithms
  •  \(b^a = c\) if and only if \(log_b(c) =a\)
  • \(log_{b} b^x = x\) for all x and \(b^{log_{b} x} = x \) for x > 0
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