LSP 121

1
LSP 121

• Logarithms

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What 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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Example Sound

• Sound has unique properties, such as the Inverse
  Square Law for Sound
• This law states that sound from a speaker gets
  spread over a larger and larger area as it moves
  farther from the speaker
• This area increases with the square of the
  distance from the speaker
• For example, at 1 meter, the area might be 1 sq
  meter at 2 meters, it is 4 sq meters

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Sounds

• The threshold of human hearing is considered 1
  (100)
• The rustle of leaves is 10 times louder than the
  threshold of hearing (101)
• A whisper is 100 times louder than the threshold
  of hearing (102)
• Busy street traffic is 108 times louder than the
  threshold of hearing

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Decibel

• These 10n values are clumsy to work with, so they
  created the term decibel (one tenth of a bel)
• A sound 108 is actually 80 decibels (dB)
• A sound 101 is 10 dB
• Or loudness in dB 10 log10 (intensity of sound
  / intensity of softest audible sound)

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Dangerous Sounds

• A rock concert is typically around 100 - 120 dB
  (depends on where you sit/stand)
• The threshold of pain for the human ear is around
  120 dB
• Immediate perforation of the eardrum is 160 dB

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Log Base 10

• The log base 10 (written log10) is a very common
  log
• log10 x is the power to which 10 must be raised
  to obtain x
• Or better yet, 10 to what power equals x?
• log10 1000 ? (10 to what power 1000?) 3
• log10 10,000,000 7
• log10 0.1 -1
• log10 30 1.4777

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Log Base 2

• The log base 2 (written log2) is a very common
  log when dealing with computers (since computers
  use the binary number system which is base 2
  arithmetic)
• log2 x is the power to which 2 must be raised to
  obtain x
• Or better yet, 2 to what power equals x?

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Log Base 2

• Log2 32 5
• Log2 1024 10
• Log2 40 5.32
• Dont have Log2 on your calculator? Take Log10
  of the same value and then divide by 0.301