64.8k views
1 vote
What is log₁ (logarithm with base 1) equal to?
a) 1
b) 0
c) 10
d) none

1 Answer

0 votes

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.

User DavidVdd
by
8.0k points

Related questions

asked Aug 1, 2024 96.3k views
JaAnTr asked Aug 1, 2024
by JaAnTr
8.5k points
1 answer
5 votes
96.3k views