2^(2^x) = 16^(16^16)

Рет қаралды 5,782

Prime Newtons

Күн бұрын

Пікірлер: 30

@alexzuma2025 5 күн бұрын

16^^3 = 16^(16^16) tetration is also written with a double up arrow.

@jaybazu 5 ай бұрын

Brilliant spirit will always encounter opposition from mediocre spirits... That is so far established.. Bro you look like a bass player I know but bass players aren't stupid incapable of understanding math... Whatever you look like you are great and you know that stuff... Keep teaching us

@michaelz2270 5 ай бұрын

Another way of looking at it: You want log_2(log_2(16^16^16)). First logarithm log_2(16^16^16) equals 16^16 log_2(16) = 4 * 16^16. Second iterated logarithm gives log_2(4 * 16^16) = log_2 4 + log_2 16^16 = 2 + log_2 16^16 = 2 + 16 log_2 16 = 2 + 16*4 = 66.

@TavinTong-f8p 2 ай бұрын

I agree with what he says…🎉

@CC--qn4gf 5 ай бұрын

They thought evaluating a tetration from bottom to top made a big number, little did they know lol. Btw if anyone is interested I found a formula that you can use for just that; evaluating from bottom to top. Formula such that 'a' is equal to the base and 'n' is equal to the hyperpower: a^^n = a^(a^(n-1))

@X-SHOTA 5 ай бұрын

Hi there ! I have got a problem for you can you please make a video solving it ? the problem is : prove that for all strictly positive reel numbers a and b : (2ab) / (a+b) + sqrt( (a² + b²) / 2 ) >= (a + b) / 2 + sqrt(ab)

@PrimeNewtons 5 ай бұрын

You're the second person to recommend this problem. I'll work on it .

@Sigma.Infinity 4 ай бұрын

Looks like the AM/GM and or Cauchy-Schwarz Inequality methods may be useful.

@Noor-kq9ho 5 ай бұрын

2^2^x = 16^16^16 => 2^2^x = (2⁴)^16^16 => 2^2^x = 2^4(16^16) => 2^x = 4(16^16) => 2^x/4 = 16^16 => 2^x/2^2 = 16^16 => 2^(x-2) = 16^16 => 2^(x-2) = (2^4)^16 => 2^(x-2) = 2^(4•16) => 2^(x-2) = 2^64 => x-2 = 64 => x = 64+2 x = 66

@dawkinsfan660 4 ай бұрын

Tetration is associative only on the right, but not on the left.

@V-The_Present 5 ай бұрын

This is actually teached in f.2

@xinpingdonohoe3978 5 ай бұрын

And what is f.2?

@V-The_Present 5 ай бұрын

@@xinpingdonohoe3978 grade 8

@_Heb_ 5 ай бұрын

@@xinpingdonohoe3978Whatever it is, they don't teach English grammar in it

@robertveith6383 5 ай бұрын

* *taught*

@V-The_Present 5 ай бұрын

@@robertveith6383 ok ty

@pojuantsalo3475 5 ай бұрын

Interestingly I got completely different answer: 16^16^16 = (2^4)^16^16 = (2^2^2)^16^16 = 2^2^(2*16^16) ==> x = 2*16^16 = 2*2^64 = 2^65. Not sure where this goes wrong. It is so easy to make a mistake with these exponent towers and it doesn't help the size of these numbers is beyond comprehension.

@numero17171 5 ай бұрын

I belive the mistake happens after the third "=", you shoud have done (2^2)*(16^16) instead of 2^(2*16^16)

@pojuantsalo3475 5 ай бұрын

@@numero17171 Yeah, I got this now. Thanks!