How can I express e to the power of the natural log of a number?

To express e to the power of the natural logarithm of a number, we can utilize the properties of logarithms and exponents. Specifically, the natural logarithm function, denoted as ln, is the inverse of the exponential function with base e.

So, if you have a number x, the expression e raised to the power of ln(x) can be simplified as follows:

eln(x) = x

This simplification occurs because the exponential function and the natural logarithm are inverses of each other. Thus, when we raise e to the power of the natural logarithm of a number, we obtain that number back.

For example, if you take x = 5, then:

eln(5) = 5

In summary, the expression e to the power of the natural logarithm of x simply yields x itself. This property is incredibly useful in various fields, including calculus, finance, and statistics, where exponential growth and decay are frequently encountered.