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Prove-that-ln-13-1-10-13-2-gt-0-without-calculator-

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Question Number 212098 by CrispyXYZ last updated on 30/Sep/24
Prove that ln (((√(13))−1)/(10)) + (√(13)) − 2 >0 without calculator.
Provethatln13−110+13−2>0withoutcalculator.
Answered by MrGaster last updated on 03/Nov/24
ln((√(13))−1)−ln 10+(√(13))−2>0 ln((√(13))−1)+(√(13))>2 in consideration of (√(13))<3(∵e^3 >10),∴ : ln((√(13))−1)+(√(13))>ln(3−1)+3 >ln2+3 >1+2 >2+ln 10 ∴, ln(((√(13))−1)/(10))+(√(13))−2>0
ln(13−1)−ln10+13−2>0ln(13−1)+13>2inconsiderationof13<3(∵e3>10),∴:ln(13−1)+13>ln(3−1)+3>ln2+3>1+2>2+ln10∴,ln13−110+13−2>0

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