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.

The value of $\log(1)$ is $0$.

The value of $\log(1)$ is $0$.

Steps to Solve

1. 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.

1. 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.

1. State the conclusion

Therefore, we can conclude that: $$\log(1) = 0$$

The value of $\log(1)$ is $0$.

• 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.