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Logarithmic Inequality Interplay (Posted on 2024-06-27)

Prove that (log₄ 20)² + (log₂ 3)² > 7

P&P solutions only, please.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 2 of 3 |

20>16=4^2, then log4(20) > log4(16)=2

9>8=2^3, then 3>2^(3/2), then log2(3) > log2(2^(3/2)=3/2

Substitute these inequalities to get

[log4(20)]^2 + [log2(3)]^2 > 2^2 + (3/2)^2 > 7

Edited on June 27, 2024, 1:01 pm

Posted by Brian Smith on 2024-06-27 12:51:31

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