Huge numbers!

Algebra Level 3

Let a = 25 12 , b = 16 14 , c = 11 16 . a={ 25 }^{ 12 },\quad b={ 16 }^{ 14 },\quad c={ 11 }^{ 16 }.

Which of the following is true?

b < c < a b<c<a a < c < b a<c<b c < a < b c<a<b b < a < c b<a<c

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2 solutions

Chew-Seong Cheong
Nov 24, 2015

\(\begin{array} {} a = 25^{12} = 5^{24} = \left(5^3\right)^8 & = 125^8 \\ b = 16^{14} = 2^{56} = \left(2^7\right)^8 & = 128^8 \\ c = 11^{16} = \left(11^2\right)^8 & = 121^8 \end{array} \)

c < a < b \Rightarrow \boxed{c < a < b}

So clever!! Expressing all numbers in terms of powers of 8

Jun Arro Estrella - 5 years, 6 months ago

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Not me, the one so set the problem is smart. I just figured out his trick.

Chew-Seong Cheong - 5 years, 6 months ago
Jun Arro Estrella
Nov 25, 2015

From PMO hoooo are you a contestant from PMO?

No, I am not. Maybe Julian is.

Chew-Seong Cheong - 5 years, 6 months ago

Yeah.. I posted a few problems from PMO on this site.

Julian Yu - 5 years, 6 months ago

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