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Understanding Logarithmic Functions: Common and Natural Logarithms Explained

This section covers logarithmic functions, focusing on the common logarithm (log base 10) and the natural logarithm (ln). It explains the equivalence between logarithmic and exponential forms, where log_b(x) = a if and only if b^a = x. You will learn how to evaluate logarithms of different bases and solve problems. Examples will guide you through calculations, and homework exercises will reinforce your understanding. Enhance your grasp of logarithms and their applications with practical examples and solutions.

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Understanding Logarithmic Functions: Common and Natural Logarithms Explained

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  1. Section 5.5 Logarithmic Functions

  2. Common Logarithm: log x = a iff 10a = x ex: log 100

  3. Other Logarithms: • Bases other than 10 can be used: logbx = a iff ba = x logex = k can be written as: ln x = k iff ek = x *** this is called the natural logarithm

  4. Ex. 1: Evaluate:

  5. Ex. 1…: Evaluate:

  6. Ex. 2: Given log 3.257 = .5128, find:

  7. Ex. 3: Given ln 2 = .69315, find:

  8. Ex. 4: Solve:

  9. Ex. 4…: Solve:

  10. Ex. 4…: Solve:

  11. Homework : pg. 194 2-22 ev, 36-44 ev Only parts a & c

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