Learning Objectives:

__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?*

*2. **What is a natural log in math?*

*3. **How do you solve for an exponent?*

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