# Solving Exponential and Logarithmic Equations

## Overview

### Description

Logarithmic equations can be solved by various methods, including converting to a common base, writing in exponential form, or raising both sides to an exponent. A multistep logarithmic equation can be simplified to a one-step equation by using properties of logarithms, and then it can be solved.

Exponential equations can be solved by writing in logarithmic form or by taking the log of both sides. A multistep exponential equation can be simplified to a one-step equation by using properties of exponents, and then it can be solved.

Logarithmic equations and exponential equations are often used in real life and can be solved using a graphing calculator.

### At A Glance

• A simple logarithmic equation can be solved by using an equality property of logarithms or by writing the equation in exponential form.
• A multistep logarithmic equation can be solved by using properties of logarithms and then using an equality property or writing in exponential form.
• Some logarithmic equations can be solved by using substitution to change the form of the equation.
• Logarithmic equations can be solved by graphing the related functions for both sides of the equation and looking for points of intersection.
• Exponential equations can be solved by using equality properties of exponential expressions or by using the relationship between exponents and logarithms.
• Some exponential equations can be solved by using substitution to change the form of the equation.
• Exponential equations can be solved by graphing the related functions for both sides of the equation and looking for points of intersection.