Find the Domain y = log base a of x

Problem

y=(log_a)(x)

Solution

1. Identify the definition of the logarithmic function. The expression (log_a)(x) represents the exponent to which the base a must be raised to produce the value x

2. Apply the constraints for the base a For the function to be defined as a standard real-valued function, the base must be positive and not equal to one, so a>0 and a≠1

3. Determine the restriction on the argument x Since any positive base a raised to any real power always results in a positive number, the argument x must be strictly greater than zero.

4. Express the domain in interval notation. The set of all valid input values x is the set of all positive real numbers.

Final Answer

Domain: *(0,∞)

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