Inspired by Sandeep sir

Algebra Level 4

A = 2 2315 , B = 5 997 , C = 3 1461 \Large A=2^{2315}, \quad B=5^{997}, \quad C=3^{1461}

Given the values of A , B A,B and C C , which of these inequalities in the answer choices must be true?

Inspiration .

B > C > A B>C>A C > A > B C>A>B A > B > C A>B>C A > C > B A>C>B C > B > A C>B>A

Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Using TI calculator 3 1461 2315 = 2.000377427 > 2. ⟹ C > A 2 2315 997 = 5.000131016 > 5 ⟹ A > B C , A , B Can any one help me solving without a calculator ? \Large 3^{\frac {1461}{2315}}=2.000377427~>~2. \implies~C~>~A\\\Large 2^{\frac {2315}{997}}=5.000131016~>~5~~\implies~A~>~B\\\Huge C,A,B\\~~\\\text{Can any one help me solving without a calculator ?}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Sir, I come up with solution by applying logarithm.

Syed Shahabudeen - 5 years, 9 months ago

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Perfectly OK.

Niranjan Khanderia - 5 years, 9 months ago

Me too on the logarithms...but i verified with a calculator

Greg Grapsas - 3 years, 5 months ago

Me too yee

Isaac YIU Math Studio - 1 year, 10 months ago

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