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- Feb 14, 2012

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Prove $\dfrac{1}{\log_2 \pi}+\dfrac{1}{\log_5 \pi}>2 $.

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,599

Prove $\dfrac{1}{\log_2 \pi}+\dfrac{1}{\log_5 \pi}>2 $.

- Mar 31, 2013

- 1,283

= $\log_{\pi} 2 +\log_{\pi} 5$ using $\log_a b * \log_b a = 1$

Now $\pi = 3.14 < 3.15$

so $\pi^2 < 31.5^2$ or $\pi^2 < 992.25$ as $31 * 32 = 992$

so $ 10 > \pi^2$

so we have

$\log_{\pi} 10 > 2$ and hence the result

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