natural logarithm
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AI overview
The natural logarithm is a mathematical tool that answers the question "what power do I need to raise the number e to in order to get this result?" — it's essentially the reverse of exponential growth involving e, one of math's most important constants. It matters because exponential processes involving e appear everywhere in nature and science, from population growth to radioactive decay, making the natural logarithm essential for solving real-world problems.
AI-generated from the Wikipedia summary — may contain errors.
Article
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.
The natural logarithm of x is the power to which e would have to be raised to equal x. For example, ln 7.5 is 2.0149..., because e = 7.5. The natural logarithm of e itself, ln e, is 1, because e = e, while the natural logarithm of 1 is 0, since e = 1.