exponential

Level 1

Which one is bigger??

2^100 or 3^98 ??

3^98 2^100

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2 solutions

Siddharth Singh
May 31, 2015

( 2 + 1 ) 98 > 2 98 + 98 2 97 1 = 2 97 ( 2 + 98 ) = 2 97 100 (2+1)^{98}>2^{98}+98*2^{97}*1=2^{97}(2+98)=2^{97}*100

2 97 100 > 2 97 50 > 2 97 2 5 = 2 102 2^{97}*100>2^{97}*50>2^{97}*2^{5}=2^{102}

3 98 > 2 102 > 2 100 3^{98}>2^{102}>2^{100}

Therefore, 3 98 > 2 100 3^{98}>2^{100}

Sunil Pradhan
May 31, 2015

2^100 or 3^98 ?

2^100/100 or 3^98/100 ?

2^1 or 3^0.98 ?

0.98 is approximately equal to 1

2^1 or 3^1 ?

2^1 < 3^1

3^98 > 2^100

No, that approach doesn't exactly work.

Calvin Lin Staff - 6 years ago

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