Solving Exponential and Logarithmic Equations

There are two basic strategies for solving exponential and logarithmic equations:

1. One-to-One Properties

• if and only if
• if and only if

2. Inverse Properties

• 
• 

Strategies for solving Exponential and Logarithmic Equations

1. Rewrite the given equation in a form to use the One-to-One properties
2. Rewrite an exponential equation in logarithmic form and apply the Inverse Property
   
3. Rewrite a logarithmic equation in exponential form and apply the Inverse Property
   

For Example:



(One-to-One property)






Now you have to check your answers to make sure they are not negative (due to domain restrictions). We find that 6 works, however 1 does not.

Another example that we need to know:




Let





now substitute

and

and