Natural Logarithm (ln) Calculator

Understanding Natural Logarithm (ln)

The natural logarithm, denoted as $$ln(x)$$ or $$log_e(x)$$, is the logarithm to the base $$e$$, where $$e$$ is an irrational and transcendental number approximately equal to 2.71828. It is fundamental in calculus and many areas of mathematics, physics, and engineering.

Formula: The natural logarithm of a number $$x$$ is the power to which $$e$$ must be raised to equal $$x$$. Mathematically, if $$y = ln(x)$$, then $$e^y = x$$.

Example: To calculate the natural logarithm of 10 (ln(10)), you are asking: "To what power must $$e$$ be raised to equal 10?". Using this calculator, you'll find that ln(10) ≈ 2.3026. This means $$e^{2.3026} \approx 10$$.

Use Cases: Natural logarithms are used in various fields, including:

• Calculating exponential growth and decay.
• Solving problems in compound interest and finance.
• Analyzing radioactive decay in physics.
• Modeling population growth in biology.
• In information theory and statistics.