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

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Find the value of x?
How to solve 3^x-1 + x = 5
In this video, we'll show you How to Solve Math Olympiad Question A Nice Algebra Problem 3^x-1 + x = 5 in a clear , fast and easy way. Whether you are a student learning basics or a professtional looking to improve your skills, this video is for you. By the end of this video, you'll have a solid understanding of how to solve math olympiad exponential equations and be able to apply these skills to a variety of problems.
#matholympiad #maths #math #algebra

[@pspprabhat]

3^×-1=-×+5
=>1=(-×+5)(3^-×+1)
=>(3^4)ln3=(-×+5)ln3
.e^ln3(×+1+4)
=>W{3ln3.e^ln3(3)}
=W{(-×+5)Ln.e^ln3(-×+5)}
By applying Lambert 5:57 w-function..w(a.e^a)=a
=>3ln3=(-×+5)ln3
=>×=5-3=2*

[@SALogics]

Very nice! ❤

[@davidseed2939]

3^(x-1) is monotonic increasing
5-x is monotonic decreasing.
so there is only one real solution
x=2 is clearly that sole real solution.

[@SALogics]

Very nice! ❤

[@wes9627]

3+2=5

[@SALogics]

Very nice! ❤

[@diegosimonetti9496]

il risultato è x = 2
n.b. : è stata utilizzata la formula W di Lambert

[@SALogics]

Very nice! ❤