Find the Domain and Range log base 2 of x

Problem

(log_2)(x)

Solution

1. Identify the restriction for the logarithmic function. The argument of a logarithm must be strictly greater than zero.

2. Determine the domain by setting the argument x>0 In interval notation, this is (0,∞)

3. Analyze the behavior of the function to find the range. As x approaches 0 from the right, (log_2)(x) approaches −∞ As x approaches ∞ (log_2)(x) approaches ∞

4. Conclude that the function takes on all real values, meaning the range is (−∞,∞)

Final Answer

Domain: *(0,∞), Range: *(−∞,∞)

Want more problems? Check here!