Introduction: Exponential and Logarithmic Equations

Wild rabbits in Australia. The rabbit population grew so quickly in Australia that the event became known as the "rabbit plague." (credit: Richard Taylor, Flickr)

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.

The learning objectives for this lesson include:

• Identify an exponential equation whose terms all have the same base
• Idenitfy cases where equations can be rewritten so all terms have the same base
• Apply the one-to-one property of exponents to solve an exponential equation
• Use logarithms to solve exponential equations whose terms cannot be rewritten with the same base
• Solve exponential equations of the form  [latex]y=A{e}^{kt}[/latex] for t
• Recognize when there may be extraneous solutions, or no solutions for exponential equations
• Use the definition of a logarithm to solve logarithmic equations
• Use a graph to verify or analyze the solution to a logarithmic equation
• Solve half-life problems
• Solve pH problems

The learning activities for this lesson include:

• Read: Exponential Equations with Like Bases
• Self-Check: Exponential Equations with Like Bases
• Read: Exponential Equations with Unlike Bases
• Self-Check: Exponential Equations with Unlike Bases
• Read: Logarithmic Equations
• Self-Check: Logarithmic Equations
• Read: Applied Exponential and Logarithmic Equations
• Self-Check: Applied Exponential and Logarithmic Equations

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