A number theory problem by fred fan

Number Theory Level 1

Which would be bigger, 7 7 66 77^{66} , or 6 6 77 66^{77} ?

6 6 77 66^{77} 7 7 66 77^{66}

Fred Fan by fred fan , 21, Canada

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1 solution

Fred Fan
May 26, 2015

All we need to figure out is what is bigger, (6^7)^11, or (7^6)^11. Since they both have the same power, we just have to find which one would be bigger, 6^7, or 7^6. This way would be an easier way to find out which would be bigger.

1 Helpful 0 Interesting 0 Brilliant 2 Confused

That argument is completely wrong.

  1. 77^66 is not equal to ( 6 ^ 7)^11.

  2. 2 ^3 < 3 ^2, but 22^33 > 33^22.

Calvin Lin Staff - 6 years ago

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