Understanding logarithms as inverse exponentials

The  exercise appears under the Algebra II Math Mission. This exercise explores the relationship between logarithms and exponentials.

Types of Problems
There are three types of problems in this exercise:


 * 1) Write the exponential as a logarithm and vice versa: This problem has a logarithmic and exponential expression. The student is asked to transfer both into the other type of form.Ulaie1.png
 * 2) Fill in the missing values: This problem has a chart that has the inputs and outputs of a exponential and related logarithmic function. The student is asked to fill in the missing values.Ulaie2.png
 * 3) Plot the points on the inverse function: This problem has a graph with several points. The student is asked to plot the points that would be on the inverse function.Ulaie3.png

Strategies
Knowledge and experience with logarithms and exponentials are encouraged to ensure success on this exercise.
 * 1) The expression $$log_{b}a=c$$ is equivalent to $$b^c=a$$.
 * 2) No calculator is needed for the Fill in the missing values problem. The inputs and outputs above and below each other are just reversed.
 * 3) The point on an inverse function is (y,x) if the point (x,y) is on the original function.

Real-life Applications

 * 1) Practice with logarithms increase ability with exponents.
 * 2) Logarithms are useful in many scales, such as Richter, Decibel and pH.