Math Olympiad Question | Equation solving | You should learn this trick to pass the exam

Equation solving with best tricks ever and excell in exams!

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[phoebe]

For everyone who thinks she's wrong here's an explanation.

The issue here is that when she introduces the rule in the first step in her solution (a^m)^n = a^m×n
but the problem on the page is
a^m^n = a^(m^n)
She also says "whenever" you have a power to a power you multiply the powers (which is not true) so it appears that she's going to treat the problem as x^4x but she's actually introducing the rule because she's about to raise (x^x^4)^4 and then rewrite it as (x^4)^x^4 = 8^8
So, x^4 = 8
x = 4root8

She did a very bad job of explaining and seems to have mispoken so it's got people more confused than before watching the video. So possibly not the best teaching moment!

[jim]

The key is in raising to exponent 4 on both sides, the 4 on the LHS goes on the x downstairs for (x^4)^(x^4).
So we've got (x^4)^(x^4) = 8^8. Then it's application of a^a = b^b having equal bases. x = 8^(1/4).

[arungupta]

There is an ambiguity in the problem. The solution given is for x raised to (x raised to 4). But what about (x raised to x) raised to 4?

Note that the brackets matter.

E.g., (5 raised to 3) raised to 2 is (5 raised to 6), while 5 raised to (3 raised to 2) is (5 raised to 9).

[sharonnoel]

Take log to the base 64 and differenciate wrt x

[대구선비]

In real number, it is correct. But In Complex number, we need to have 2 addtional solution.
x = +-(8)^^(1/4), +-(8)^^(1/4)i

[steffenhantschel]

The trick is at 1:30, but you don´t get any hint before, so you couldn´t understand the steps before.

[haiyangwan]

Whilst the written narrative shows what the speaker is thinking, some of the spoken narration is incorrect (eg "64 can be written as 8 squared OVER 4") which makes it a bit difficult to follow . In addition at 1:38 saying "now we can compare either the bases or the powers" and then going on immediately to say "Thus we have X^4 = 8" is moving a bit fast. Nothing is said about what was found as a result of making this comparison (ie that both the bases and the exponents are the same on both sides of the equation). It seems to be taken a obvious that if a^a = b^b then a = b. Whilst a=b is one solution to this, it is not obvious (to me at least) that there are not other solutions.

Does anyone have a proof that a^a = b^b implies a = b?

[ShedrachCodded]

I know it is correct, but I'm confused totally of the way it is solved

[abcd]

This is wrong....the question is x power x power 4 which is different from x power x4

[mrmimi]

You write the equation wrongly
It's supposed to be

(x^x)⁴ not x^x^4


If we assumed x = 3 then the first one equals:

(2^2)⁴ = 4⁴ = 256


And the second one equals:

2^2^4 = 2^16 = 65256

[k.lakshmi]

😂😂😂
Simple math
Consider x power 4 = a
x^a = 2^8
Then a = 8
So, finally x power 4 = 8.

[vikramsharma]

Wrong. The powers are at different level and you cannot multiply them. Your logic is correct but your notation is wrong.