Idon't know how to get the answer, but i've been given the answer and it's x=ln 8.

E^2x - 5e^x = 24

(e^x)^2 - 5e^x =24

let e^x = u

u^2 - 5u = 24

u^2 -5u - 24 =0

(u - 8)(u+3)=0

u = 8 or u = -3

since e^x = u then u can't equal -3

e^x = 8

by taking ln for both sides

ln(e^x) = ln(8)

xln(e) = ln(8) ln(e) = 1

x = ln(8) = 3ln(2)