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Logarithms
LSP 120
Logarithms
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
Logarithms
What 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
Logarithms
What is a Logarithm?
Log 10 X means…
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log101000 = 3 because
Log1010,000 = 4 because
log1010,000,000 = 7
log1030 = 1.477 because
log10300 = 2.477 because
…the Power to which 10 is
raised to get X
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103 = 1000
104 = 10000
107 = 10,000,000
101.477 = 30
102.477 = 300
So in general … log b X = Y because bY = X
Logarithms
Conversions
 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
Logarithms
Two Important Log Rules
1. log 10x = x
2. log ax = x * log a
 This rule used with exponential functions
 Logs used to solve for exponent variable
 Want to learn more? Click here.