Math Olympiad | A Nice Algebra Problem | A Nice Exponential Equation

[@AyushPandey-n6s]

Congratulations sir for 1k subscribe

[@SALogics]

Many many thanks! ❤

[@prollysine]

let u=2^x , by fakt. , u^3 +/- x^2 - x -120=80 , (u-5)(u^2+5u+24)/2 , u=5 , u^2+5u+24=0 , u=(-5+/-V(25-96))/2 ,
+1 -5 u= (-5+/-V(25-96))/2 , (-5+/-i*V(71))/2 ,
5 -25 u= (-5+i*V(71))/2 , (-5-i*V(71))/2 , u=2^x , 2^x=5 , x=log5/log2 ,
24 -120=0 , test , 8^(log5/log2)-2^(log5/log2)=125-5 , --> 120 , OK ,
solu , x= 5 , (-5+i*V(71))/2 , (-5-i*V(71))/2 ,

[@SALogics]

Very nice! ❤