1. Exponential Functions Show that any exponential function in the form f(x) = ca^x can be written as f(x) = Ce^kx. That is, write k in terms of a. Use your method to write g(x) = 2^x in the form e^kx for some k.

2. Solve each equation.

(a) 5(1.4)^x - 4 = 25

(b) 4^2-x = 4^2x+1

3. Solve each equation.

(a) 5 log₂ 2x = 25

(b) ln (x + 1) + ln (x - 1) = ln 3