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How It Works
The natural logarithm ln(x) uses base e ≈ 2.71828 and is the inverse of the exponential function. If y = ln(x), then e^y = x. This calculator solves both directions: enter x to find ln(x), or enter y to find e^y.
Example Problem
Find ln(7.389):
- We need the power y such that e^y = 7.389.
- Since e² ≈ 7.389, ln(7.389) ≈ 2.
Frequently Asked Questions
What is the value of e in natural log?
Euler's number e ≈ 2.71828 is an irrational constant that appears throughout mathematics. It is the base of the natural logarithm and the natural exponential function. ln(e) = 1.
How to convert natural log to log base 10?
Divide by ln(10) ≈ 2.3026. So log₁₀(x) = ln(x) / 2.3026. For example, ln(100) ≈ 4.605, and 4.605 / 2.3026 = 2, which is log₁₀(100).
Where is the natural logarithm used?
Natural logs appear in compound interest, population growth, radioactive decay, and many differential equations. Any process with continuous exponential growth or decay is naturally described using ln and e.
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- Radioactive Material Calculator — apply exponential decay, the inverse of the natural log.