This is cool, always wondered how you would operate with Power Towers since Bobby first mentioned them to me. A while back now I know
]]>That is fine work. But that is not how I do it. I am a very good guesser, watch this:
Cool hah!
]]>Whew! we made it.
Taller towers would be even more complicated!
]]>I am sure you know how now!
Tower powers are my favorite.
You are right, D is larger it is easier to see that by this:
while
Now you can see that D is the man by inspection.
]]>Which of the following class-4 numbers is larger?
C = 2^2^2^83 (The ^ means to the power of.)
D = 3^3^3^52
as before we take the logarithm of both but this time we must do it twice, and we find
ln(ln(C)) = ln(ln(2)) + [ln(2) * 9671406556917033397649408]
= 6703708186976009930559261.24579...
ln(ln(D)) = ln(ln(3)) + [ln(3) * 6461081889226673298932241]
= 7098223961595389530659098.10481...
so D is larger.
(I see that 2^83 is the long 96714... number above, but I don't get how to get the log parts.)