ln 0 equals
Understand the Problem
The question is asking for the value of the natural logarithm of 0. To solve this, we need to understand the properties of logarithmic functions in mathematics.
Answer
Undefined
Answer for screen readers
The natural logarithm of 0 is undefined.
Steps to Solve
- Understanding the natural logarithm function
The natural logarithm, denoted as $\ln(x)$, is the logarithm to the base $e$, where $e$ is an irrational number approximately equal to 2.71828.
- Define the natural logarithm of a positive number
The natural logarithm function $\ln(x)$ is only defined for positive values of $x$. For any $x > 0$, $\ln(x)$ gives the power to which $e$ must be raised to equal $x$. Mathematically, $e^y = x$ implies $y = \ln(x)$.
- Consider the natural logarithm at 0
As $x$ approaches 0 from the positive side, the value of $\ln(x)$ decreases without bound. This means $\ln(x) \to -\infty$ as $x \to 0^+$. Therefore, $\ln(0)$ is not defined and is considered $-\infty$ in the limit approach.
Therefore, the natural logarithm of 0 is negative infinity, but formally, we say that $\ln(0)$ is undefined.
The natural logarithm of 0 is undefined.
More Information
The natural logarithm function is only defined for positive values of x, and as x approaches 0 from the positive side, ln(x) approaches negative infinity.
Tips
A common mistake is to think that ln(0) has a finite value or is simply 0. Remember, ln(x) is undefined for non-positive values of x.
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