590,295,810,358,705,651,712 according to Wolfram Alpha.
what is 2 to the power of 69
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Dec 31, 2023
0
#4
The answer has to be 1 modulo 7, which deraprince"s is, so I think Wolfram is correct on this occasion.
Wolfram Alpha is insanely good at math, so I would venture to say it's correct on a simple calculation like 2^69.
Also, 2^10 is just over 10^3, so it stands to reason that 2^70 would be a fair bit over 10^21, meaning 2^69 would be a fair bit larger than 5*10^20, which dearprince's number is.
Jan 13, 2024
0
#7
You can even google it (i.e. type 2^69 in your browsers omnibox), but it will give the approximate answer in scientific notation: 5.9029581e+20. Of course W|A or any other math software get that right, even Python has now unlimited size integers and is on almost any computer su you can just run Python (Windows-R then 'python') and type 2**69 (as in FORTRAN for those who know).
Yes, also 2^10 = 1024 = 10^3 + 2.4%, so 2^20 = 10^6 + 4.8% etc, more generally 2^x ~ 10^(0.3 x) where the 0.3 is log10 2 = .30102999566 ~ .30103 ~ 0.3 (the middle one is easy to remember and then 3 -> 2999, too...) and 69 x .3 = (70-1) x .3 = 21.0 - .3 = 20.7 and 10^.7 ~ 5 = 10/2 again because .7 = 1 - log10 2.
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