Olympiad Mathematics | Solve and Check Exponential Equation | Math Olympiad Training

Can you solve this given exponential equation for X with nested exponents. Also check the answer for any extraneous solution.

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Olympiad Mathematics | Solve and Check Exponential Equation | Math Olympiad Training

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[annapiamazzeo]

Fantastic video! As always, your explainations are extremely clear and simple to follow. Congrats!!!!

[jaybling]

First step was setting 2^3^4^x = 512. Then acknowledging that 512 = 2^9. So 2^3^4^x = 2^9. With the same base, we can say 3^4^x = 9. We know that 9 = 3^2 so 3^4^x = 3^2. With the same base, we can say 4^x = 2. We know that 2 is the square root of 4 so x = 1/2.

[anatoliy]

Enormous multidecker exponential equation and its step-by-step power decreasing! I like so much equations like this. Thanks a lot for your lessons and your words of care and support, Mr PreMath. God bless you!

[ralkadde]

First and foremost, I really appreciate your channel and the kind you lead us to the solutions.
As x is on the top, we can evaluate x in one step:
x = log4 (log3 (log2 (512))) = log4 (log3 (9)) = log4 (2) = ½.
But as I see your solution do not need logarithms, only comparisons. That is fine.

[sugaruisland]

Thank you so much, sir. I could enjoyed solving this problem. After finding your YouTube Channel, I tried to solve many questions of yours, I'm not so much good at algebra, there are not a few failures. But they really heal me because I'm suffering from insomnia. Today, I'm very happy I could solve 8 problems. And I'm going to read René Decartes this evening. Thank you very much from Japan. Good night! Arigato-gozaimashita (this is Japanese word for English "Thank you very much."

[fevengr]

It looked intimidating but turned out to be easy. Thanks!

[arthur_p_dent]

At first glance, without having watched the clip: 2^9=512 (having memorized the powers of 2 up to 2^10 sure helps)

therefore 3^4^x = 9

therefore, and since 3²=9: 4^x = 2

2 is the square root of 4, in other words 2 = 4^(1/2); therefore, x=1/2.

Took longer to write down than it did to figure out.

[SuperYoonHo]

Wonderful solution!!! I loved the way you did it!

[michaelstahl]

Thank you for a great job. Checking solution was very well !

[Bestmix]

Thanks a lot premath for helping me understanding Difficult math problems

[nsengiyumvaamidu]

Guys you are really helping me a lot to improve my skills, may God bless you a lot❤⚘

[shadmanhasan]

Gonna work on this later, but for the base fcn, it's basically 2^3^4 -> either it's = 8^4, which is basically (64×64), or 2^27, which is a VERY large number.

[HappyFamilyOnline]

Amazing explanation👍
Thank you so much for this wonderful video💕💕

[davidfromstow]

I had the right answer but because it was1/2, I thought I must be wrong! Thank you, as always, especially for the proof.

[plkrishh]

I could get the Answer X=1/2 by mental calculations. Thanks to all earlier videos in pre math.

[hemaldoshi]

The answer can also be 3/4 sins x^n^m = x^n*m

[robertpenoyer]

This is simple. 2^3^4^x needs to turn into 2^9. But 3^2 is 9, so 4 needs to turn into 2. Taking the square root of 4 yields 2, so x = 1/2.

[GodbornNoven]

8^(4^x)= 512
log 8 both sides

4^x = 3
log_4 both sides
x= log_4 of 3

[sarveshdhiman]

can you solve this 2^2^2^x - 256 = 0 ? Base on the calculation as you did in the video. Please reply.
as we all know 2^8 = 256.
But according to your explanation this will be written as
2^2^2^x = 2^8, then
2^2^x = 8, because the base is same, then
2^2^x = 2^3, then
2^x = 3, because the base is same, then
what would be the value of 'X' here. Please reply with the answer or inform me if I'm not doing it as per the video explanation ?

[alster]

This is another example of solving an exponential equation via _Chain Rule_

Tricky but easy