3.2: Exponential simultaneous equations and reciprocal exponential

0606/11/M/J/24 — Question 9 · 9 marks

(a)
Solve the following simultaneous equations.
ex+y×e3x2y=1e^{x + y} \times e^{3x - 2y} = 1x2y=256x^{2}y = 256
[5]
(b)
Solve the equation 10e2x111=6e12x10\mathrm{e}^{2x - 1} - 11 = 6\mathrm{e}^{1 - 2x}, giving your answer in exact form.
[4]