voodoo_child wrote:How to find whether How to find whether 7^5 is > or < 5^7?
Similarly, 101^25 and 25^101? Thoughts? What's an easy way to guesstimate such questions ?
Compare POWERS OF 10 and BALLPARK.
2^10 = 1024 ≈ 10³.
Case 1: 7^5 <--> 5^7:
(7²)(7²)(7)(2^7) <--> (5^7)(2^7)
(50)(2)(50)(2)(7)(2^5) <--> 10^7
(10^4)(200) <--> 10^7
(10^6)(2) <--> 10^7
Since the righthand side is greater, 5^7 > 7^5.
Case 2: 101^25 and 25^101
(10²)^25 <--> (5²)^100
(10^50)(2^200) <--> (5^200)(2^200)
(10^50)(2^10)^20 <--> 10^200
(10^50)(10³)^20 <--> 10^200
10^110 <--> 10^200
Since the righthand side is greater, 25^101 > 101^25.
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