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ISP 121

ISP 121. 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. What is a Logarithm?.

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ISP 121

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  1. ISP 121 Logarithms

  2. 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

  3. 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”

  4. Converting and Solving log525 = y 5y = 25 Y = 2 log525 = 2 log5125 = y 5y = 125 Y = 3 log5125 = 3 log3 27 = y 3y = 27 y = 3 So log3 27 = 3 log7 49 = y 7y = 49 y = 2 So log7 49 = 2

  5. Log Base 10 • The log base 10 (written log10 or just log) is a very common log • log10x is the power to which 10 must be raised to obtain x • Or better yet, 10 to what power equals x?

  6. 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

  7. 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 Log2.5 = .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 = 2x = 100 log x = 3 x = 1000 log x = 6 x = 100,000

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