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# Logarithms ISP 121.

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Logarithms ISP 121

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? 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”

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

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?

Log Base 10 Solve the following without a calculator: log = y 10y = 100 102 = 100 log = 2 Log = y 10y = 1000 103 = 1000 log = 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

Log Base 10 Review the answers.
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 = Log = y log =

Log Base 10 log 2.5 = y Log 2.5 = .39794 So what is log 25? Log 250?
Use what we learned in the last slide. Remember, log = log10 log 2.5 = y Log 2.5 = So what is log 25? Log 250? Log 25000? log 25 = log 250 = log 2500 = 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

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