Addressing the power tower equation 2^3^4^x=512

Added: 2026-05-31

[00:00:00]That's absolutely wrong. 12x is equal  to 9. X is equal to 3 over 4. Okay, I want to go over this equation with you guys  again, which is from my YouTube short. We have the power tower equation. 2 to the 3r to the 4  to the x power is equal to 512. It's a notation that caused the confusion sometimes. So if you see  this, well, are we trying to say we have 2 to the 3 and then to the 4th and then to the x? That's  equal to 512. Hm. If you look at it like this, then yes, we can multiply the exponents together.  We do get 2 to the 3 * 4 is 12 * x. So 12 x and 512 just like the good old days that you  have the 512 megabyte USB flash drive and some of you guys mentioned the 512k RAM. But  anyways, either way, two to the 9th power. Well, we have two to something. So, that implies the  exponents have to be equal. And then divide both sides by 12. Reduce the fraction. Yes, you do  end up with 3 over 4. However, that was only if the question was written like this. two to  the 3 and then with parentheses to the 4th and then parenthesis to the x power then yes you can  multiply it like that with the exponents. However, if the question was written like this means by the  usual convention we actually look at this exponent first. So we're looking at 2 to the 3r to the 4th  to the x as this 4 to the x power worked out first and then do 3 to that power and then two to that  power and al together you end up with 512. This thing actually means that not this not this. So if  you have this situation then you have to break it down as 2 to the3r to the 4 to the x equals 512 is  2 to the 9. So this has to be the same as that. So 3 to the 4 to the x is equal to 9 and 9 is the  same as 3 to the second power. So this has to be the same as that because 3 to some power right.  So implies four to the x is equal to two. And then depends on how you want to solve it from here. If  you want to be fancy a little bit, you can look at the two as four to the 1/2 power because the  half power is the same as taking the square root.

[00:02:47]It's not multiplying this and that together. It's  a square root of four which is gives you the two.

[00:02:52]Then you can see this it's the same as that. So  the conclusion is x is equal to 12. So based on what the question was written originally, this is  the correct solution and this is yeah that's it.