# Section 4.5 - Exponential and Logarithmic Equations

**Section Objectives**

- Solve exponential equations.
- Solve logarithmic equations.
- Use and solve exponential and logarithmic equations in applications.

### Two Important Properties for Solving Equations

Some kinds of logarithmic and exponential equations can be solved by appealing to the **one-to-one property** of logarithms and exponentials:

In order to use these properties, (1) the equation must be written with a single term on each side of the equation, and (2) each side must have an expression in the same base.

#### Examples

Other equations can be solved by using the properties of logarithms and exponentials. The following examples are typical.