a. Given that a^x ≡ e^kx, where a and k are constants, a > 0 and x ∈ R, prove that k = ln a.

b. Hence, using the derivative of e^kx, prove that when y = 2^x dy/dx = 2^x ln 2

c. Hence deduce that the gradient of the curve with equation y = 2x at the point (2, 4) is ln 16.