Logarithmic and Exponential Functions

By Mukongori Uncategorized

About Course

Exponential functions and logarithm functions are important in both theory and practice. In this unit we look at the graphs of exponential and logarithm functions, and see how they are related. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. After reading this text, and/or viewing the video tutorial on this topic, you should be able to:

• specify for which values of a the exponential function f(x) = a x may be defined,                                                             • recognize the domain and range of an exponential function, • identify a particular point which is on the graph of every exponential function, • specify for which values of the logarithm function f(x) = log a x may be defined, • recognize the domain and range of a logarithm function, • identify a particular point which is on the graph of every logarithm function,   • understand the relationship between the exponential function f(x) = e x and the natural logarithm function f(x) = ln x.

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What Will You Learn?

  • Given any logarithmic function, learners should be able to find its domain and range accurately.
  • Given a natural logarithmic function, learners should be able to evaluate limits and deduce relative asymptotes accurately.
  • Given a natural logarithmic function, learners should be able to differentiate it accurately.
  • Given a natural logarithmic function, learners should be able to study the variation and sketch its curve perfectly.
  • Given a logarithmic function with any base, learners should be able to find the domain and range accurately.
  • Given a logarithmic function with any base, learners should be able to find limits and deduce its relative asymptotes accurately.
  • Given a logarithmic function with any base, learners should be able to find its derivative accurately.
  • Given a function containing more complicated products and quotients, learners should be able to differentiate it moderately.
  • Given a logarithmic function with any base, learners should be able to study the variation and sketch its curve accurately.

Course Content

Logarithmic and Exponential Functions

  • Domain and range of natural logarithmic functions
    22:44
  • Limit and asymptotes for natural logarithmic functions
    13:19
  • Derivative of natural logarithmic functions
    14:37:00
  • Variation and curve sketching of natural logarithmic functions
    22:44:00
  • Domain and range of logarithmic function with any base
    13:19
  • Limit of logarithmic function with any base
    36:53:00
  • Logarithmic differentiation
    36:54:00
  • Further logarithmic differentiation
    23:45:00
  • Variation and curves of logarithmic functions with any base
    40:48:00

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