Solve the equation for w ezw 3ew z 0Solutione2w 3 ew 2

Solve the equation for w e^zw - 3e^w + z = 0

e^2w - 3 e^w + 2 = 0

let e^w = x

the equation now becomes

x^2 - 3x + 2 = 0

factoring the equation

(x-2)(x-1) = 0

x = 2

x = 1

substituting back x= e^w

we get

e^w = 2

taking natural log on both sides

w ln e = ln 2

w = ln 2

e^w = 1

w ln e = ln 1

w = ln 1

w = 0

solutions are

w = 0 , 0.6931