Brazil | A Nice Algebra Problem | Math Olympiad

[@ronbannon]

Very nice job.

[@SALogics]

Thank you so much! ❤

[@ronbannon]

Nice problem and excellent explanation of using the W function to solve for x.

[@SALogics]

Thanks for liking! ❤

[@فیروزاهنگری]

3×3^(3x)=3^2/x , 3^(3x-1)=2/x=k ,
2/x=k , x=2/k then
3^(3×2/k-1)=k , 3^[(6-k)/k then
3=k^[k/(6-k)] ,
3^[3/(6-3)]=k^[k/(6-k)] so. k=3
x=2/k , x=2/3

[@ronbannon]

Very nice, indeed.

[@SALogics]

Very nice! ❤

[@pspprabhat]

3×.(3^3)^×=2(3^2)
W{3×.Ln3.e^ln3(3×)}
=W{2ln3.e^ln3(2)}
=>3×ln3=2ln3
=>3×=2,×=2/3

[@SALogics]

Very nice! ❤

[@pspprabhat]

(3^3×)=18/3×=6/×
=>1/6=(×.3^-3×)
=>-3/6=(-3×)Ln3.e^ln3(-3×)
=>(-1/2)ln3=
=W{(-3×)Ln3.e^ln3(-3×
.e^ln3(-3×)}

[@SALogics]

Very nice! ❤