Find the Domain y = log of 12*144

Problem

y=(log_)(12⋅144)

Solution

1. Identify the function type. The given expression y=(log_)(12⋅144) is a constant function because it does not contain any variables.

2. Evaluate the argument of the logarithm. The argument is 12⋅144 which equals 1728

3. Determine the condition for the domain. For a logarithmic function (log_)(u) the domain is defined by the requirement that the argument u must be greater than zero.

4. Check the argument. Since 1728>0 the expression is defined for all real values of any implied independent variable.

5. Conclude the domain. Since there is no variable x in the expression, the function is a constant defined everywhere. In the context of real-valued functions, the domain is the set of all real numbers.

Final Answer

Domain: *(−∞,∞)

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