1. What is Inverse Natural Log?

The inverse natural log, also known as the exponential function, is the mathematical operation that reverses the natural logarithm. Given a number x, the inverse natural log is calculated as e^x, where e is Euler's number (approximately 2.71828).

2. How Does the Calculator Work?

The calculator uses the exponential function:

Where:

• \( e \) — Euler's number (approximately 2.71828)
• \( x \) — Input value (unitless)
• \( Inverse \) — Result (unitless)

Explanation: The exponential function calculates the value of e raised to the power of x, effectively reversing the natural logarithm operation.

3. Importance of Inverse Natural Log Calculation

Details: The inverse natural log is fundamental in mathematics, physics, engineering, and finance. It's used in exponential growth/decay models, compound interest calculations, and solving differential equations.

4. Using the Calculator

Tips: Enter any real number value for x. The calculator will compute e^x and display the result. Both input and output are unitless quantities.

5. Frequently Asked Questions (FAQ)

Q1: What is Euler's number (e)?
A: Euler's number is a mathematical constant approximately equal to 2.71828. It's the base of the natural logarithm and appears in many areas of mathematics.

Q2: What's the difference between inverse natural log and regular exponentiation?
A: Inverse natural log specifically uses e as the base, while regular exponentiation can use any base number.

Q3: Can I calculate inverse natural log for negative numbers?
A: Yes, the calculator accepts negative values for x. e^x will always be positive regardless of whether x is positive or negative.

Q4: What are some practical applications of inverse natural log?
A: Applications include population growth modeling, radioactive decay calculations, continuous compound interest, and signal processing.

Q5: How accurate is the calculator?
A: The calculator uses PHP's built-in exp() function, which provides high precision for most practical applications.