ISP 121

1
ISP 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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What is a Logarithm?

• Logarithms are exponents in disguise.
• The output of a logarithm is an exponent
• log b X Y ? bY X
• The first equation is in log form and the
  second equation is in exponent form

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Converting and Solving

• log3 27 y
• 3y 27
• y 3
• So log3 27 3
• log7 49 y
• 7y 49
• y 2
• So log7 49 2

log525 y 5y 25 Y 2 log525 2 log5125
y 5y 125 Y 3 log5125 3
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Log Base 10

• The log base 10 (written log10 or just log) 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?

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Log Base 10
Solve the following without a calculator

• log10 100 y
• 10y 100
• 102 100
• log10 100 2
• Log10 1000 y
• 10y 1000
• 103 1000
• log10 1000 3

log10 10,000 y 104 10,000 log10 10,000
4 Log10 10,000,000 y 107 10,000,000 log10
10,000,000 7
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Log Base 10
Solve the following with a calculator
Review the answers. With log base 10, how do the
answers change when x is multiplied by 10? y
increases by 1 For log base 10, when y
increases by 1, x is multiplied by 10

• log10 3 y
• log10 3 .4771
• Log10 30 y
• log10 30 1.4771
• Log10 300 y
• log10 300 2.4771

8
Log Base 10
Use what we learned in the last slide. Remember,
log log10

• log 2.5 y
• Log 2.5 .39794
• So what is log 25?
• Log 250?
• Log 25000?
• log 25 1.39794
• log 250 2.39794
• log 2500 4.39794

Log x 1 101 10 X 10 So what is x if log x
2? what is x if log x 3? what is x if log x
4? what is x if log x 6? log x 2 x 100 log
x 3 x 1000 log x 6 x 100,000