Indian l can you solve this?? l Olympiad Math Exponential Problem

[@prollysine]

let u=(3/2)^x , u^2-3u+1=0 , u=(3+/-V(9-4))/2 , u= (3+V5)/2 , (3-V5)/2 , --> , (3/2)^x= (3+V5)/2 , x1=log((3+V5)/2)/log(3/2) ,
x^2=log((3-V5)/2)/log(3/2) , test x1 , 8.38535=8.38535 , OK , test x2 , -11.9256 not same 11.9256 --> not a solu ,
solu , x= log((3+V5)/2)/log(3/2) ,