Why is e ln 2 equal to 2?

To understand why e^{ln 2} equals 2, we need to break down the mathematical expressions. The symbol e represents Euler’s number, which is approximately 2.71828, and is the base of the natural logarithm.

The natural logarithm function, ln, is the inverse of the exponential function with base e. This means that when we take e raised to the power of the natural logarithm of a number, we essentially retrieve that number. In mathematical terms, this is expressed as:

eln x = x

In our case, we’re looking at ln 2, so we can substitute x with 2:

eln 2 = 2

This equation holds true because the logarithmic function and the exponential function are inverses of each other. Therefore, when you evaluate e^{ln 2}, you simply get 2.

In conclusion, e^{ln 2} = 2 due to the property of logarithms and exponentials being inverse functions.