Using logarithms to solve exponential equations

The  exercise appears under the Algebra II Math Mission. This exercise introduces the process for isolating a variable from an exponent.

Types of Problems
There is one type of problem in this exercise:


 * 1) Solve the exponential equation: This problem has an exponential equation. The student is asked to write the answer as an exact solution using logarithms, and also find a decimal approximation.Ultsee1.png

Strategies
Knowledge of logarithms and an ability to use them to solve equations are encouraged to ensure success on this exercise.
 * 1) The exact forms do not need to be simplified by logarithmic rules.
 * 2) Exact forms can be found mentally but isolating the exponential, taking a logarithm, then dividing by the appropriate constant.
 * 3) The decimal form should be rounded to the thousandths place.

Real-life Applications

 * 1) Using logarithms to solve equations are useful for finding the time when particular values happen in growth models.
 * 2) Operations, such as exponentiation need to be undone, and logarithms are the way to undo exponentiation.