An exponential equation is an equation in which a variable appears in the exponent.
To solve exponential equations, we can use the following methods:
- Rewriting the bases to be the same.
- Using logarithms.
Solving Exponential Equations by Rewriting the Bases
If the bases of the exponential terms can be rewritten to be the same, we can solve the equation by equating the exponents.
NoteThis method only works when the bases can be rewritten to be the same. If not, we need to use logarithms.
Solving Exponential Equations Using Logarithms
When the bases cannot be rewritten to be the same, we can use logarithms to solve the equation.
TipWhen using logarithms, you can use any logarithm base (e.g., \$\log_{10}\$ or \$\ln\$) as long as you use the same base on both sides of the equation.
Solving Exponential Equations with Multiple Terms
For equations with multiple exponential terms, we may need to combine the methods above.
Theory of KnowledgeHow do logarithms help us solve exponential equations? What does this tell us about the relationship between exponential and logarithmic functions?
