Final answer:
Logarithm with base 1, log₁, is undefined because the base of a logarithm must be a positive real number not equal to 1. Since 1 raised to any power is always 1, it does not satisfy the essential requirement for a base in a logarithmic function.
Step-by-step explanation:
The logarithm with base 1, commonly referred to as log₁, is actually undefined. The reason behind this is that for any base b, logarithm log_b(a) is defined only if b is a positive real number not equal to 1, because the function y = bⁿ (where n is any real number) is constant when b equals 1. Therefore, the function does not have an inverse, which would be the logarithmic function. Logarithms are based on exponential functions, and in the case of log₁(x), we can't find a number that 1 can be raised to in order to get any number other than 1, as 1 raised to any power is always 1. So, the answer to the student's question is d) none.