1. Logarithms LSP 120

2. 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

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

4. Logarithms What is a Logarithm? log 10 1000 = 3 because Log 10 10,000 = 4 because log 10 10,000,000 = 7 log 10 30 = 1.477 because log 10 300 = 2.477 because 10 3 = 1000 10 4 = 10000 10 7 = 10,000,000 10 1.477 = 30 10 2.477 = 300 Log 10 X means… …the Power to which 10 is raised to get X So in general … log b X = Y because b Y = X

5. Logarithms Conversions  Should know how to convert from  Log form to exponent (log b X = Y)  Exponent form to log ( b y = X)  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

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