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Question Number 191795 by 073 last updated on 30/Apr/23
3x−2x=19x=??
Commented by mr W last updated on 30/Apr/23
weknow27−8=19,i.e.33−23=19thereforex=3.thereisnoothersmartmethodyoucanblindlyapplytocalculatetheroot.forexampleyoucan′tsolve3x−2x=20exactly.
Answered by deleteduser1 last updated on 30/Apr/23
x=3Itremainstoshowthatnoothersolutionexists3x=2x+19;obviously,ifthereexistsanotherxThenx>3Observethatddx(3x)=3xIn(3)andddx(2x+19)=2xIn(2)Andsince3xIn(3)>2xIn(2)forx>33x>2x+19forx>3.Thetwocurvesneverintersectagain.Hence,x=3istheonlysolution.
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