2 What is a Logarithm?A logarithm (or log) is a number that represents a power or exponentWhy use logs?A simpler way to express large valuesSome 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 exponentlog b X = Y ↔ bY = XThe first equation is in “log form” and the second equation is in “exponent form”
5 Log Base 10The log base 10 (written log10 or just log) is a very common loglog10 x is the power to which 10 must be raised to obtain xOr better yet, 10 to what power equals x?
6 Log Base 10Solve the following without a calculator:log = y10y = 100102 = 100log = 2Log = y10y = 1000103 = 1000log = 3log10 10,000 = y104 = 10,000log10 10,000 = 4Log10 10,000,000 = y107 = 10,000,000log10 10,000,000 = 7
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 1For log base 10, when y increases by 1, x is multiplied by 10log10 3 = ylog10 3 = .4771Log10 30 = ylog10 30 =Log = ylog =
8 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 = log10log 2.5 = yLog 2.5 =So what is log 25?Log 250?Log 25000?log 25 =log 250 =log 2500 =Log x = 1101 = 10X = 10So 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 = 100log x = 3 x = 1000log x = 6 x = 100,000