## Tutoring on Solving Logarithmic Equations

Learning Objectives:

#### Understand to Solve Logarithmic Equations.

Math Tutoring on Solving Logarithmic Equations

There are really two types of log equations the first type is when you have an equation that has only two logs of the same base.  If that is the case, we set the logs equal to each other. Then it follows that the argument of the first log must equal the argument of the second log. So we will set those equal to each other and then solve. Now, we do have to check our answers, because the argument of the log has to be greater than zero. So if we obtain a value that makes this less than or equal to zero, we have to exclude it.  Now, there are guidelines for solving the more general type of log equation and here are the steps.

1. If there is more than one log, combine them using the properties of logs and then we need to isolate the single log.

2. Then we are going to write the equation in exponential form.

3. We need to solve and check.

The properties that we do have to be aware of are the product property, quotient property, and power property. Also sometimes it can be the case of base formula.  The main reason for checking these is the argument of the log has to be greater than zero and if it is not, it would not be a solution.

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Hook Questions:

1.    How do you get rid of the natural log?

3.    How do you solve for an exponent?

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