Learning Outcomes
By the end of this lesson, you will be able to:
- Solve an exponential equation with a common base.
- Rewrite an exponential equation so all terms have a common base then solve.
- Recognize when an exponential equation does not have a solution.
- Use logarithms to solve exponential equations.
- Solve a logarithmic equation algebraically.
- Solve a logarithmic equation graphically.
- Use the one-to-one property of logarithms to solve a logarithmic equation.
- Solve a radioactive decay problem.
In 1859, an Australian landowner named Thomas Austin released 24 rabbits into the wild for hunting. Because Australia had few predators and ample food, the rabbit population exploded. In fewer than ten years, the rabbit population numbered in the millions.
Uncontrolled population growth, as in the wild rabbits in Australia, can be modeled with exponential functions. Equations resulting from those exponential functions can be solved to analyze and make predictions about exponential growth. In this section we will learn techniques for solving exponential and logarithmic equations.