Olympiad Mathematics Question || Solving Olympiad Exponential Equation

In this solution to Olympiad mathematics question, you will learn how to solve tough exponential equations with easy. You will equally be introduced to how you can solve for the imaginary roots of any exponential equation applying Euler's equation and other mathematical rules. You will gain a complete understanding of the Euler's identity otherwise know as the most beautiful equation.
Here, you will also learn about the factorization method of solving quadratic equations step-by-step.

#exponents #exponentialequations #onlinemathstv

[koestermeinhart]

i found the value of x by testing x = 2; you not only showed exact way how to find x=2, but also the second complex value of x by making clever use of Euler equation, thank you

[orlandovaldes]

Si quieres aprender más de matemática física y química, sígueme.

[jamesmorton]

What you did was rigorous and shed light on Euler's identity . e^πi+1=1

[hardsg]

I dont think the second solution is right...elaborate if i miss anything.thanks

[Zbigniew-bu]

Kochanieńki ! za dużo pisaniny, to równanie rozwiązałem w jednej linijce, łącznie z zespolonym, bo 9^x-1=(3^x+1)(3^x-1), a ln(-1)=Pi*i

[Yes_I_cn]

Cheers mate.
But at the same time, 3^x+1 cannot be zero (you cannot divide by zero), so the imaginary solution is not an actual solution to que original problem, correct?

Note: I didn't exactly use Euler's identity per si, in order to solve the problem and find the 2nd theoretical solution, but wrote -1 in polar coordinates instead, which is basically the same thing as using Euler's identity.

[andytsai]

I am a Taiwanese, watching this random video at my 3AM😂While I would go to work at 9AM😂Why am I here
How about make 9^x-1 equals to (3^x+1)*(3^x-1), and then literally divide 3^x+1, we got 3^x-1=8, thus x=2; Considering 3^x+1=0 for a expectation, thus x=blablabla

[RamkrishnaAre]

This can be solved very easly. Let me explain

9 to power of x - 1 can be split into. (3 to power of x +1) ( 3 to power of x -1)

Finally we are getting. 3 to power of x - 1 = 8; then 3 to power of x-1= 3 to square; x =2
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