One of the easiest topics to comprehend is logarithm specifically the range and domain of logarithmic function. The graph of a logarithmic function is the reflection of an exponential function. The range and domain of the graph of this function is critical to understand how this function behaves. Given a logarithmic function where b>1 and U>0. Any values of and the function does not exist.

**Sample Problem 1:**

Find the range and domain of

The range of the function is the set of all real numbers, in symbol

For the domain of the function we just need to focus on U in logU. In this example,

Since U>0, or x-2>0 or x>2. In symbols

**Sample Problem 2: **

Find the range and domain of

Range:

Domain: the explanation is the same as mentioned above.

**Sample Problem 3:**

Find the range and domain of

Range:

Domain: >0. or <0. This time, you need to have a skill to solve quadratic inequality. The roots are -3 and 3 and in this form of quadratic equation the solution set or the Domain is (-3,3)

**Sample Problem 4:**

Find the range and domain of .

Range:

Domain: >0. The roots of this equation are 1 and 2. The solution set of this quadratic inequality is . This is also the domain.

**Challenge:**

Direction: Find the Range and Domain of the following

1.

2.

3.

4.

5.

1. Range: ; Domain:

2. Range: ; Domain:

3. Range: ; Domain:

4. Range: ; Domain:

5. Range: ; Domain: