The inverse relationship of exponents and logarithms

The  exercise appears under the Algebra II Math Mission. This exercise practices solving various problems that focus on the relationship between $$a^x=b$$ and $$\log_{a}(b)=x$$.

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.The inverse relationship of exponents and logarithms.PNG
 * 2) Fill in the missing values: This problem has a chart that contains the inputs and outputs of an exponential and related logarithmic function. The student is asked to fill in the missing values.The inverse relationship of exponents and logarithms2.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.The inverse relationship of exponents and logarithms3.PNG

Strategies
Knowledge and experience with logarithms and exponentials are encouraged to ensure success while doing this exercise.
 * 1) The expression $$\log_{b}a=c$$ is equivalent to $$b^c=a$$.
 * 2) No calculator is needed for the second type of problem. The inputs and outputs above and below each other are only 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.