perplexus.info :: Just Math : What BIG is bigger?

What BIG is bigger? (Posted on 2023-07-03)

BIG1=63^9
BIG2=33^11

Which of the BIGs is bigger?

No calculating aids, just p&p

See The Solution Submitted by Ady TZIDON

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Puzzle Solution

| Comment 3 of 4 |

BIG1 = 63^9 = 3^9*21^9= 3^9*3^9*7^9=3^18*7^9

BIG2 = 33^11 = 3^11*11^11

Hence :

BIG1 vs BIG2

--> 3^18*7^9 vs 3^11*7^9

--> 3^7*7^9 vs 11^11

Now, 3* 7^3 =1029 < 1331 =11^3

Or, 3^3*7^9< 11^9

and, 3 ^4 =81 < 121 = 11^2

Hence,

3^7*7^9 <11^11

Therefore, , BIG2 is bigger.

Posted by K Sengupta on 2023-07-03 09:45:51

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