# 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.

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