What is the value of log 1?
Understand the Problem
The question is asking for the value of the logarithm of 1 (log 1). The logarithm of any number is the exponent to which the base must be raised to produce that number. Since any number raised to the power of 0 is 1, we can conclude that log 1 equals 0.
Answer
The value of $\log(1)$ is $0$.
Answer for screen readers
The value of $\log(1)$ is $0$.
Steps to Solve
- Identify the base of the logarithm
In most cases, if the base is not specified, we assume base 10 for common logarithms or base $e$ for natural logarithms. However, for the purpose of this problem, we focus on the property of logarithms.
- Apply the logarithm property
We will apply the fundamental property of logarithms that states: $$ \log_b(1) = 0 $$ This is because any base $b$ raised to the power of 0 gives us 1.
- State the conclusion
Therefore, we can conclude that: $$ \log(1) = 0 $$
The value of $\log(1)$ is $0$.
More Information
This is a key property of logarithms. The logarithm of 1 is always zero, regardless of the base used. This concept is crucial in various branches of mathematics and is often used in exponential equations and calculus.
Tips
- Confusing the logarithm of a number less than 1: Some might mistakenly think that $\log(1)$ should yield a negative value or any other number, but it is always 0.
- Forgetting the base of the logarithm: When calculating logarithms, it's important to identify the base, although in this case, it doesn't change the conclusion since $\log(1)$ is 0 for any base.
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