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Question Number 56477 by problem solverd last updated on 17/Mar/19

let x and y be two real numbers if x+y≤10 prove ln(x+1)+ln(y+1)≤2ln6

letxandybetworealnumbersifx+y⩽10proveln(x+1)+ln(y+1)⩽2ln6

Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

x+y≤10 (x+1)+(y+1)≤12 (((x+1)+(y+1))/2)≥(√((x+1)((y+1))) 6≥(√((x+1)(y+1))) 36≥(x+1)(y+1) ln(36)≥ln(x+1)+ln(y+1) 2ln6≥ln(x+1)+ln(y+1)

x+y⩽10(x+1)+(y+1)⩽12(x+1)+(y+1)2⩾(x+1)((y+1)6⩾(x+1)(y+1)36⩾(x+1)(y+1)ln(36)⩾ln(x+1)+ln(y+1)2ln6⩾ln(x+1)+ln(y+1)

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