log 1 1
Understand the Problem
The question is asking for the value of the logarithm of 1 with base 1. The logarithm is a mathematical function that determines the exponent to which the base must be raised to obtain a certain number.
Answer
$0$
Answer for screen readers
The final answer is $0$.
Steps to Solve
-
Identify the logarithm expression
We want to evaluate the logarithm of 1 with base 1, which is expressed as:
$$ \log_1(1) $$ -
Understanding the logarithm definition
The logarithm $\log_b(a)$ is defined as the exponent $x$ such that:
$$ b^x = a $$
In our case, we need to find $x$ such that:
$$ 1^x = 1 $$ -
Evaluate the exponent
Any number, including 1, raised to the power of 0 is equal to 1. Therefore:
$$ 1^0 = 1 $$
Thus, $x = 0$ satisfies the equation. -
Conclude the value
Hence, we can conclude that:
$$ \log_1(1) = 0 $$
The final answer is $0$.
More Information
The logarithm with base 1 is unique because the base itself does not change regardless of the exponent. Logarithm functions are usually defined for bases greater than 0 and not equal to 1 because of these peculiar properties.
Tips
- A common mistake is assuming that the logarithm is undefined for $\log_1(1)$. However, in this specific case, it yields a value.
- Confusing the concept of logarithms with an undefined exponent or base.
