Question Number 1112 by malwaan last updated on 14/Jun/15
$${compare}\:\frac{\mathrm{1}}{{log}_{\mathrm{2}} \pi}\:+\:\frac{\mathrm{1}}{{log}_{\mathrm{5}} \pi}\:{and}\:\mathrm{2} \\ $$
Answered by prakash jain last updated on 15/Jun/15
$$\mathrm{log}_{\pi} \mathrm{2}+\mathrm{log}_{\pi} \mathrm{5}=\mathrm{log}_{\pi} \mathrm{10} \\ $$$$\mathrm{10}>\pi^{\mathrm{2}} \Rightarrow\mathrm{log}_{\pi} \mathrm{10}>\mathrm{2} \\ $$