e to the natural log of x equals what?

• A. 1/x
• B. x
• C. ln x
• D. e^x

Answer: (B)

The key idea is that exponential and logarithmic functions are inverses of each other. The natural log ln x is defined as the exponent to which e must be raised to get x (for x > 0). So e^(ln x) = x, since you’re undoing the logarithm by applying the same exponential base. That’s why the expression simplifies to x. The other options don’t fit because they represent different values: 1/x would result from a different operation, ln x is the exponent itself, and e^x would require the exponent to be x instead of ln x.