Solve the exponential equation | (Math Olympiad Training) #math #maths

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Solve the exponential equation | (Math Olympiad Training) #math #maths

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

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[yalchingedikgedik]

Thanks Sir .
Thanks PreMath.
Good luck.

[gelbkehlchen]


Solution:
(1/216)^(2x) = x |*216)^(2x) ⟹
x*216^(2*x) = 1 = 1/6*216^(2*1/6) |The same operations are done with x on the left side of the equation as with 1/6 on the right side of the equation, therefore ⟹ x = 1/6

[lifeisamarathon]

we can take log with base 6 to solve the problem...we can get it easily

[misterenter-izrz]

6^(-6x)=x, 6^(-6)=x^(1/x), (1/6)^6=×^(1/x), therefore x=1/6.😊

[nineko]

As soon as I saw the 216 I knew that a 6 had to be involved in some way 😁

[rachelraja]

How do u prove if a^a equals b^b then a=b

[silverhammer]

Now...try it with something that doesn't have integer roots 🤔😵‍💫

[WhiteGandalfs]

Hmmm... well.. This is a typical "dick length comparison" task: It shows that the inventor has a dick length of "able to handle power expressions" and the practical usage scale of very close to absolute ZERO. I would recommend using this as an extremely simplified example for the typical task of cryptography to EASILY generate a ciphertext but make it exceptionally HARD to solve it. In this specific case, for this specific simplification of the solution, you have to guess the IDEA of the creator for the creation of the involved constant. Else you have to take a generalized approach, which is a multitude harder.