Logarithms ISP 121 What is a Logarithm A

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 ↔ b. Y = X • The first equation is in “log form” and the second equation is in “exponent form”

Converting and Solving log 3 27 = y 3 y = 27 y=3 So log 3 27 = 3 log 525 = y 5 y = 25 Y=2 log 525 = 2 log 7 49 = y 7 y = 49 y=2 So log 7 49 = 2 log 5125 = y 5 y = 125 Y=3 log 5125 = 3

Log Base 10 • The log base 10 (written log 10 or just log) is a very common log • log 10 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 10 100 = y 10 y = 100 102 = 100 log 10 100 = 2 Log 10 1000 = y 10 y = 1000 103 = 1000 log 10 1000 = 3 log 10 10, 000 = y 104 = 10, 000 log 10 10, 000 = 4 Log 10 10, 000 = y 107 = 10, 000 log 10 10, 000 = 7

Log Base 10 Solve the following with a calculator: log 10 3 = y log 10 3 =. 4771 Log 10 30 = y log 10 30 = 1. 4771 Log 10 300 = y log 10 300 = 2. 4771 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

Log Base 10 Use what we learned in the last slide. Remember, log = log 10 log 2. 5 = y Log 2. 5 =. 39794 So what is log 25? 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