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2-x-2-x-1-gt-3-x-3-x-1-

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Question Number 191210 by TUN last updated on 20/Apr/23
2^x +2^(x+1) >3^x +3^(x+1)
2x+2x+1>3x+3x+1
Answered by ARUNG_Brandon_MBU last updated on 20/Apr/23
2^x +2^(x+1) >3^x +3^(x+1) ⇒2^x (1+2)>3^x (1+3) ⇒3.2^x >4.3^x ⇒2^(x−2) >3^(x−1) ⇒(x−2)ln2>(x−1)ln3 ⇒(ln2−ln3)x>2ln2−ln3 ⇒x < ((2ln2−ln3)/(ln2−ln3)) (∵ ln2−ln3 <0)
2x+2x+1>3x+3x+1⇒2x(1+2)>3x(1+3)⇒3.2x>4.3x⇒2x−2>3x−1⇒(x−2)ln2>(x−1)ln3⇒(ln2−ln3)x>2ln2−ln3⇒x<2ln2−ln3ln2−ln3(∵ln2−ln3<0)

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