Question

solve for x.

xe^x = 9

Answer 1

ln (x e^x) = lnx + x = ln9 = 2.19722

This cannot be solved algebraically in closed form.
Solve by iteration:
If x = 1, lnx + x = 1
If x = 2, lnx + x = 2.69315
If x = 1.5, lnx + x = 1.90547
If x = 1.65, lnx + x = 2.1507
If x = 1.67, lnx + x = 2.18282
If x = 1.68, lnx + x = 2.19879
If x = 1.678, lnx + x = 2.19560
If x = 1.679, lnx + x = 2.19720
If x = 1.67902, lnx + x = 2.19723
If x = 1.679013, lnx + x = 2.19722
x = 1.679013..