A Very Nice Math Olympiad Problem | Solve for x

[@robert8552]

I'm speachless

[@Lemda_gtr]

Great job 👏

[@SpencersAcademy]

Thank you! Cheers!

[@prollysine]

/:x^ln4 , 1+x^(ln10-ln4)=x^(ln25-ln4) , 1+x^(ln10/4)=x^(ln25/4) , 1+x^(ln5/2)=x^(ln25/4) ,
(5/2)^2=25/4 , x^(ln25/4)=2*(ln5/2) , 1+x^(ln5/2)=x^(2*ln5/2) , let u=x^(ln5/2) ,
u^2-u-1=0 , u=(1+/-V(1+4))/2 , u= (1+V5)/2 , / (1-V5)/2 < 0 , not a solu / , x^(ln5/2)=(1+V5)/2 , lnx=ln((1+V5)/2)/(ln5/2) ,
x=e^(ln((1+V5)/2)/(ln5/2)) , x=~ 1.69045 , test , x^ln4 +x^ln10 = 5.42202 , x^ln25 = 5.42202 , OK ,

[@SpencersAcademy]

Great job 👏