# Range and Domain of Logarithmic Function

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

[toggle title=”Solution”]

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 [/toggle]

**Sample Problem 2: **

Find the range and domain of

[toggle title=”Solution”]

Range:

Domain: the explanation is the same as mentioned above. [/toggle]

**Sample Problem 3:**

Find the range and domain of

[toggle title=”Solution”]

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)

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**Sample Problem 4:**

Find the range and domain of .

[toggle title=”Solution”]

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.

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**Challenge:**

Direction: Find the Range and Domain of the following

1.

2.

3.

4.

5.

[toggle title=”Answer key:”]

1. Range: ; Domain:

2. Range: ; Domain:

3. Range: ; Domain:

4. Range: ; Domain:

5. Range: ; Domain: [/toggle]

### Dan

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