Question 977126
Which of the following is the greatest?
a. {{{3^210}}}
b. {{{7^140}}}
c. {{{17^105}}}
d. {{{31^84}}}  
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3^210 = 9^105, obviously less than 17^105, so a is eliminated.
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Using a calculator:
7^140 = 2.059e118
17^105 = 1.57e129
31^84 = 1.88e125
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c wins again.
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You can change them all to the same base, eg, 7, but that would require either logs or a calculator.
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eg,
7^140 = (2^2.8)^140 = 2^392
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ooooooooooooooh, John's answer is cool.
I might have figured that out eventually.
I should have spotted that 3, 7, 17 & 31 are all 2^n plus or minus 1.
In short, his solution is elegant.
Probably with assistance from Satan, since we all know god is stupid.