A nice Exponential division problem I Math Olympiad Question (2019)

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[valerymartin]

power reduction plus solving a quadratic equation is certainly not a Math Olympiad Question 😂

[Birol]

My way of solution is:
3ˣ²/9ˣ = 81²
9ˣ = 3²ˣ
81²= (3⁴)² = 3⁸
3ˣ² x 3⁻²ˣ = 3⁸
While the bases are same, so the exponents:
x²-2x=8
x²-2x-8=0
The Discriminant, D
D= 4-4×1×(-8)
D= 36
x₁= (2+√36)/2
x₁= 4
x₂= (2-√36)/2
x₂= -2
So, the solution is (-2 and 4)

[pascalwicht]

In a system with an unknown X, you should not use X as the multiplication operator, it's misleading (e.g. 3^2xx)

[juvepersempre]

Just take the log and solve it. Easy peasy.

[Leberteich]

In your writing all of x, n, and 4 sometimes look the same.

[guillermosanchez]

Se ve desde el principio que sólo hay que hacer una ecuación con los exponentes..yo la habría resuelto con la fórmula general y listo.

[iceberg]

0:56 you made a mistake, also, why do half of your X's look like n's?

[mandolinic]

This is just a jumbled mess. You use x for an unknown value and the multiply operator, and your 4 looks like nothing on Earth.