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Question Number 1112 by malwaan last updated on 14/Jun/15

compare (1/(log_2 π)) + (1/(log_5 π)) and 2

$${compare}\:\frac{\mathrm{1}}{{log}_{\mathrm{2}} \pi}\:+\:\frac{\mathrm{1}}{{log}_{\mathrm{5}} \pi}\:{and}\:\mathrm{2} \\ $$

Answered by prakash jain last updated on 15/Jun/15

log_π 2+log_π 5=log_π 10  10>π^2 ⇒log_π 10>2

$$\mathrm{log}_{\pi} \mathrm{2}+\mathrm{log}_{\pi} \mathrm{5}=\mathrm{log}_{\pi} \mathrm{10} \\ $$$$\mathrm{10}>\pi^{\mathrm{2}} \Rightarrow\mathrm{log}_{\pi} \mathrm{10}>\mathrm{2} \\ $$

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