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

[@maths01n]

Added my subscription ❤❤my fellow Mathematician content creator 🎉🎉

[@SALogics]

Thanks and welcome! ❤

[@patk5724]

Very well explained in a clear concise way to abbreviate the lambert w function structure identity... even though l haven't read or get myself abreast to the lambert w function, l really understand your clarity in explanation... Many have race the details etc.

[@SALogics]

Thanks for liking! ❤

[@dougnettleton5326]

2^(x-1) = 2x
=> 2^x / 2 = 2x
=> 2^x = 4x
=> x × log base 2(2) =
log base 2 (4x)
=> x = 2 + log base 2(x)
=> x = 4, since log base 2(4) is 2 and 2 + 2 is 4.

[@ronaldnoll3247]

X(1) = 0.3099 or x(2) = 4.0

[@SALogics]

Very nice! ❤

[@فیروزاهنگری]

2^(x-1)×1/2=(2x)×1/2
2^(x-2)=x , [2^(x-2)]^1/(x-2)=x^1/(x-2)
2=x^1/(x-2) , 4^1/2=x^1/(x-2)
4^1/(4-2)=x^1/(x-2) , x=4

[@SALogics]

Very nice! ❤❤

[@prollysine]

W(-4*ln2*e^(-4*ln2))=-ln(4x)*e^(-ln(4x)) , -4*ln2==-ln(4x) , /*(-1) , ln16=ln4x , 4x=16 , x1=4 , test x1 , 2^3=8 , 2*4=8 , OK ,
W(-ln2/4)=-ln(4x) , x=e^(-W(-ln2))/4 , x2=~ 0.309907 , 0.619814=0.619814 , OK ,

[@SALogics]

Very nice! ❤

[@prollysine]

@@SALogics Thanks!

[@trojanleo123]

x = 4

[@SALogics]

Very nice! ❤

[@AClassOldie]

how are some getting x= 0.3099?

[@dougmarshall4010]

X = 4

[@SALogics]

Very nice! ❤

[@greydawndewer]

x=4

[@SALogics]

Very nice! ❤