Exponential And Logarithmic Functions

To determine the range of the function , we must ensure that the expression inside the logarithm is positive, because the logarithm of a non-positive number is undefined in real numbers.

1. First, consider the domain of the function:
2. This simplifies to:
3. The inequality implies:
4. Thus, the function is defined for .
5. For the range, consider the function again:
6. As approaches the bounds of the domain ( or ), the expression inside the logarithm approaches 0. Thus, tends to .
7. When , we have:
8. Therefore, by considering approaching from values greater than 0 to 25 (excluding 25), the range of is:

Thus, the correct answer is None of these, as <(-∞, 2)> is not provided in the options.