Using Like Bases to Solve Exponential Equations

Now, we will look at solving exponential equations. Getting the variable out of the exponent can be tricky, but you will learn the basics first in this section.

Learning Objectives

In this section, you will:

Use like bases to solve exponential equations.
Use logarithms to solve exponential equations.
Use the definition of a logarithm to solve logarithmic equations.
Use the one-to-one property of logarithms to solve logarithmic equations.
Solve applied problems involving exponential and logarithmic equations.

Seven rabbits in front of a brick building.

Figure 1 Wild rabbits in Australia. The rabbit population grew so quickly in Australia that the event became known as the "rabbit plague".

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 functions.

Source: Rice University, https://openstax.org/books/college-algebra/pages/6-6-exponential-and-logarithmic-equations
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