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If-log-a-2-b-2-2-a-b-b-log-ab-2-1-a-1-b-when-a-gt-1-b-gt-1-




Question Number 205323 by liuxinnan last updated on 16/Mar/24
If    log_(√((a^2 +b^2 )/2)) ((a+b)/b)≥log_(√(ab)) (2/((1/a)+(1/b)))  when a>1 b>1
$${If}\:\:\:\:{log}_{\sqrt{\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}}} \frac{{a}+{b}}{{b}}\geqslant{log}_{\sqrt{{ab}}} \frac{\mathrm{2}}{\frac{\mathrm{1}}{{a}}+\frac{\mathrm{1}}{{b}}} \\ $$$${when}\:{a}>\mathrm{1}\:{b}>\mathrm{1} \\ $$
Commented by liuxinnan last updated on 17/Mar/24

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