Logarithms LSP 120 Logarithms What is a Logarithm

Logarithms LSP 120

Logarithms What is a Logarithm? Ø A logarithm (or log) is a number that represents a power or exponent Ø Why use logs? § A simpler way to express large values § Some things grow or shrink exponentially, so the log is a perfect “numbering” system

Logarithms What is a Logarithm? Ø The Exponent takes 2 and 3 and gives 8 (2, used 3 times, multiplies to 8) Ø The Logarithm takes 2 and 8 and gives 3 (2 makes 8 when used 3 times in a multiplication) Ø A Logarithm says how many of one number to multiply to get another number Ø So a logarithm actually gives you the exponent as its answer

Logarithms What is a Logarithm? Log 10 X means… • • • log 101000 = 3 because Log 1010, 000 = 4 because log 1010, 000 = 7 log 1030 = 1. 477 because log 10300 = 2. 477 because …the Power to which 10 is raised to get X • • • 103 = 1000 104 = 10000 107 = 10, 000 101. 477 = 30 102. 477 = 300 So in general … log b X = Y because b. Y = X

Logarithms Conversions Ø Should know how to convert from § Log form to exponent (logb X = Y) § Exponent form to log ( by = X) Ø Notes: § When dealing with logs of base 10 • when the X value is multiplied by 10, the outcome of the log or Y increases by 1 § Logs written without the base number • Assumed to be base 10 • We will be dealing only with log base 10 • So log is the same as log 10

Logarithms Two Important Log Rules 1. log 10 x = x 2. log ax = x * log a § This rule used with exponential functions § Logs used to solve for exponent variable Ø Want to learn more? Click here.