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100 power 101 or 101 power 100 which is greater PLEASE LIST ALL THE POSSIBLE METHODS OF SOLVING THIS. CAN THIS BE DONE USING LOGARITHMS

100 power 101 or 101 power 100 which is greater PLEASE LIST ALL THE POSSIBLE METHODS OF SOLVING THIS. CAN THIS BE DONE USING LOGARITHMS

Grade:Upto college level

2 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago

it is well known that the function x^(1/x) is strictly monotonically decreasing after x=e, therefore

100^(1/100)> 101^(1/101), raising both sides of the inequality to the power 100*101, 100^101>101^100

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Gajendra
15 Points
3 years ago
Taking log both the sides
Log100^101 - log101^100
101×2 - 100x2.004
202 > 200.4 answer
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