Logarithms and Word Problems

We will be concluding logarithms on Friday by correcting a few more word problems dealing with logarithms.

The key to tackling these questions is to change the words into an exponential function in the form y=ab^(x/n). A few points of advice:

• If you're getting caught up on the terminology, making a table of values is a very good strategy. Write down the first two or three terms, then use this information to find the equation y=ab^(x/n)
• be careful with levels of interest; remember that when something doesn't change the base is 1. So if you are gaining 8% interest the base will be (1+0.08) or (1.08). Similarly, if something is depreciating by 10% then the base will be (1-.10) or (0.9).
• Your base should NEVER be negative in the scope of these questions, so if you have a negative number as the base you messed up somewhere.
  

Solving a word problem which uses logarithms contains two distinct steps. First is deriving the exponential equations from the word problem as in the picture below.

From here you have two options: you can either work the problem out using the laws of logarithms (you have an unknown in the exponents and the bases cannot be made equal, so use logarithms). Please use more significant figures than I did -_- (4 would be sufficient)

Or you can graph the intersection points between the two graphs. If you choose to do this, the board below shows how much work would be required on the provincial exam (you have to play with your window settings a bit on the calculator to get a nice picture)

Homework is the Multiple Choice questions from the January 2005 Provincial exam handed out in class, (10-18).