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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

$\pi\approx3.1416$

$A=\dfrac{1}{log_5 19}+\dfrac{2}{log_3 19}+\dfrac{3}{log_2 19}$

$B=\dfrac{1}{log_2\pi}+\dfrac{1}{log_3\pi}$

edit :$B=\dfrac{1}{log_2\pi}+\dfrac{1}{log_{\color{red}5}\pi}$

$Prove: \,\, A < B$

$A=\dfrac{1}{log_5 19}+\dfrac{2}{log_3 19}+\dfrac{3}{log_2 19}$

$B=\dfrac{1}{log_2\pi}+\dfrac{1}{log_3\pi}$

edit :$B=\dfrac{1}{log_2\pi}+\dfrac{1}{log_{\color{red}5}\pi}$

$Prove: \,\, A < B$

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