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- Feb 14, 2012

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Prove $\ln 2>\left(\dfrac{2}{5}\right)^{\frac{2}{5}}$.

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Remember to read the POTW submission guidelines to find out how to submit your answers!

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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,909

-----

Prove $\ln 2>\left(\dfrac{2}{5}\right)^{\frac{2}{5}}$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!

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- #2

- Feb 14, 2012

- 3,909

I will give the community another week to attempt at last week's high school POTW. I welcome anyone of you who are interested in this problem to give it one more try and I am looking forward to receiving your submission!

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- Feb 14, 2012

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$\ln 2>\dfrac{29558488681560}{42643891494953}\\ \ln2>0.693147\\ (\ln2)^5>(0.693147)^5 \\ (\ln 2)^5>0.160002 \\ (\ln 2)^5>\dfrac{4}{25}\\ \ln2>\left(\dfrac{2}{5}\right)^{\frac{2}{5}}$

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