How to express e to the power of ln?

A logarithm is defined as an inverse function of exponents.

Answer: e to the power of ln can be written as e^ln(x) = x.

Let us proceed step by step.

Explanation:

Let us consider y = e^ln(x)

On applying ln to both sides we get,

ln (y) = ln e^ln(x)-----(1)

By using the log rule we can write ln e^x = x ln(e)

ln (y) = ln (x) ln (e) [ solving RHS of equation 1 and LHS remains same]

ln (y) = ln (x) [ ln (e) = 1 ]

y will be equal to x as logs with same base are equal.

As we know from our assumption that y =  e^ln(x)

Therefore, e to the power of ln can be written as e^ln(x) = x.