# High School Math : Multiplying and dividing Logarithms

## Example Questions

### Example Question #1 : Simplifying Logarithms

Simplify .

Explanation:

Using properties of logs we get:

### Example Question #2 : Simplifying Logarithms

Simplify the following expression:

Explanation:

Recall the log rule:

In this particular case,  and . Thus, our answer is .

### Example Question #3 : Simplifying Logarithms

Use the properties of logarithms to solve the following equation:

No real solutions

Explanation:

Since the bases of the logs are the same and the logarithms are added, the arguments can be multiplied together. We then simplify the right side of the equation:

The logarithm can be converted to exponential form:

Factor the equation:

Although there are two solutions to the equation, logarithms cannot be negative. Therefore, the only real solution is .

### Example Question #1 : Multiplying And Dividing Logarithms

Which of the following represents a simplified form of

Explanation:

The rule for the addition of logarithms is as follows:

As an application of this,

### Example Question #1 : Adding And Subtracting Logarithms

Simplify the expression using logarithmic identities.