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Which is larger, 99^{50} + 100^{50} or 101^{50}?  Show all your steps!

 Nov 22, 2019
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Take the Log(base 10) of: 101^50 =100.21606868913212871375940891115

 

Take the Log(base 10) of: 99^50 + 100^50 =100.20547667843520423239829164658

 

Subtract the second from the first =0.01059201069692448136111726456409

 

Raise this difference to the power of 10: 10^0.01059201069692448136111726456409

 

Answer of above calculation =1.0246888504147627173327968676126 - 1 x 100

 

2.4688850414762717332796867612636 % =~ 2.5 % .

 

That is: 101^50 is about 2.5% bigger than the sum of [99^50 + 100^50]

 Nov 22, 2019

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