Show that the equation $2(\mathrm{e}^x - 3) = \mathrm{e}^{\frac{1}{2}x}$ has only one solution and

Question

Show that the equation $2(\mathrm{e}^x - 3) = \mathrm{e}^{\frac{1}{2}x}$ has only one solution and find this value correct to $3$ significant figures.[4]

Accepted Answer

$x = 1.39$ (to $3$ s.f.)

2024 FMSS PRELIMS P2 Q1

2024 FMSS PRELIMS P2 Q1