This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math Learning Center Boise State ©2010 Logarithmic functions: week 14 Business Today’s topic is logarithms (or in short hand  logs). The concept of logs was initially developed (350 years before calculators) to make multiplication and division easier by transforming multiplication into addition and division into subtraction. Today, the use of logarithms is extensive but due to calculators, logs are no longer used for the primary purpose of turning multiplication into addition and division into subtraction. Hopefully, by knowing the basic premise as to why logs were developed, it will be easier to build an understanding for logs as throughout this activity, the relationship between multiplication and addition (division and subtraction) will be very important. Last week, the critical question was asked: Are exponential functions onetoone? (Oneto one means that for each input value there is exactly one output value and for each output value there is exactly one input value.) The purpose of this question is that any function that is oneto one has an inverse function. Exponential functions were defined as gG¡¢ £ ¤ ¥ where u ¦ ¤ ¦ U or ¤ § U If we are talking about exponential functions having inverses in the beginning of a logarithm activity, there must be a reason. That reason is that logs are precisely the inverse function of exponential functions defined as ¨G¡¢ £ ©ª« ¬ ¡ where u ¦ ¤ ¦ U or ¤ § U The ¤ in ©ª« ¬ ¡ indicates that base that we are working with. For example the specific inverse relation ships: The inverse of ¥ is ©ª« ® ¡ The inverse of ¯ ¥ is ©ª« ° ¡ The inverse of ± ² ® ³ ¥ is ©ª« ´ µ ¡ There are some easy logs to figure out by using the idea of inverse functions. Because logs and exponential functions are inverses, when we see ©ª« ® ¡ £ ¶ We need to think · £ ¡ So how does this work? Given ©ª« ® ¸ £ ¶ , think · £ ¸ this should be easy to recognize that y=2....
View
Full Document
 Fall '09
 ALINASCHIMPF
 Math, Algebra, Division, Multiplication, Logarithmic Functions, Exponentiation, Inverse function, Natural logarithm, Logarithm, Math Learning Center

Click to edit the document details