Sullivan PreCalculus Section 4.5 Properties of Logarithms

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Sullivan PreCalculus Section 4.5Properties of
Logarithms

• Objectives of this Section
• Work With the Properties of Logarithms
• Write a Log Expression as a Sum or Difference of
  Logarithms
• Write a Log Expression as a Single Logarithm
• Evaluate Logarithms Whose Base is Neither 10 nor
  e

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Properties of Logarithms
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Write the following expression as the sum and/or
difference of logarithms. Express all powers as
factors.
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Write the following expression as a single
logarithm.
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Theorem If N M, then
Theorem If , then N
M.
These properties become critical when solving
exponential and logarithmic equations, covered in
the next section.
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Most calculators only evaluate logarithmic
functions with base 10 or base e. To evaluate
logs with other bases, we use the change of base
formula.