Logarithms

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Logarithms

• LSP 120

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LogarithmsWhat is a Logarithm?

• A logarithm (or log) is a number that represents
  a power or exponent
• Why use logs?
• A simpler way to express large values
• Some things grow or shrink exponentially, so the
  log is a perfect numbering system

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LogarithmsWhat is a Logarithm?

• The Exponent takes 2 and 3 and gives 8 (2, used 3
  times, multiplies to 8)
• The Logarithm takes 2 and 8 and gives 3 (2 makes
  8 when used 3 times in a multiplication)
• A Logarithm says how many of one number to
  multiply to get another number
• So a logarithm actually gives you the exponent as
  its answer

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LogarithmsWhat is a Logarithm?

• Log 10 X means

• the Power to which 10 is raised to get X

• log101000 3 because
• Log1010,000 4 because
• log1010,000,000 7
• log1030 1.477 because
• log10300 2.477 because

• 103 1000
• 104 10000
• 107 10,000,000
• 101.477 30
• 102.477 300

So in general log b X Y because bY X
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LogarithmsConversions

• Should know how to convert from
• Log form to exponent (logb X Y)
• Exponent form to log ( by X)
• Notes
• When dealing with logs of base 10
• when the X value is multiplied by 10, the outcome
  of the log or Y increases by 1
• Logs written without the base number
• Assumed to be base 10
• We will be dealing only with log base 10
• So log is the same as log10

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LogarithmsTwo Important Log Rules

• log 10x x
• log ax x log a
• This rule used with exponential functions
• Logs used to solve for exponent variable
• Want to learn more? Click here.