Final answer:
The expression 2x can be rewritten as eln(2)x since raising e to the natural logarithm of a number returns that number itself, involving the use of logarithmic and exponential properties.
Step-by-step explanation:
The function 2x can be rewritten as eln(2)x using the properties of logarithms and exponents. This is due to the fact that e to the power of ln(a) is equal to a, which is a consequence of the definition of the natural logarithm being the inverse of the exponential function with base e. In this case, by taking the natural logarithm of 2, ln(2), and then raising e to the power of ln(2) times x, we are simply applying the exponentiation rules to get back to our original base, which is 2 raised to the power x.