Mot so bai tap pt mu va logarit hay co loi giai
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Mot so bai tap pt mu va logarit hay co loi giai

Course Number: METROPOLIT gep 101, Spring 2011

College/University: Bahcesehir University

Word Count: 1719

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Phng trnh m lgarit bi Gii h phng trnh iu kin: . Th vo phng trnh ta c : So sch vi iu kin, ta c Vy nghim ca h phng trnh l bi Gii phng trnh t Khi phng trnh tr thnh: ( tha mn . (v Do nghim ca phng trnh l : bi ). ) . Gii h phng trnh . H phng trnh bi Gii h phng trnh : t Phng trnh p s : . bi Tm tt c cc gi tr ca a bt phng trnh sau c nghim ng vi mi x: . t Bt phng trnh cho s c nghim ng Xt hm s ng...

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trnh Phng m lgarit bi Gii h phng trnh iu kin: . Th vo phng trnh ta c : So sch vi iu kin, ta c Vy nghim ca h phng trnh l bi Gii phng trnh t Khi phng trnh tr thnh: ( tha mn . (v Do nghim ca phng trnh l : bi ). ) . Gii h phng trnh . H phng trnh bi Gii h phng trnh : t Phng trnh p s : . bi Tm tt c cc gi tr ca a bt phng trnh sau c nghim ng vi mi x: . t Bt phng trnh cho s c nghim ng Xt hm s ng . Phng trnh m lgarit Ta c : Do xt bng bin thin ta c p s : bi ng . Gii bt phng trnh: . bi Gii phng trnh t Phng trnh cho (tha mn c hai phng trnh) a) (Do cng hai v li) b) p s: bi Gii bt phng trnh t th bt phng trnh tr thnh Phng trnh m lgarit h o c bi Gii bt phng trnh (1) c ngha h o c c ngha h o c Lp bng xt du ta c: - Vi - Vi - Vi th (1) v ngha th v tri (1)<0 , v phi (1)>0 , (1) sai. th (1) v ngha . - Vi th v tri (1)>0,v phi (1)<0,(1) ng - Vi nn (1) h o c , kt hp vi ta c p s : bi Gii phng trnh . Tp xc nh Phng trnh t Phng trnh Ta c h p s: bi Gii phng trnh . Phng trnh m lgarit . t Gii phng trnh trn ta c bi Gii phng trnh . . t Gii phng trnh trn ta c bi . Gii phng trnh Tp xc nh H trn v nghim => tp xc nh l tp rng Vy phng trnh cho v nghim bi Gii bt phng trnh : Bt phng trnh cho tng ng vi bi Cho phng trnh (1) Tm phng trnh (1) c t nht mt nghim thuc on . (1) iu kin . t ta c (2) Vy (1) c nghim khi v ch khi (3) c nghim Cch 1. Hm s l hm tng trn on [1;2]. Ta c c nghim . Cch 2. TH1. Phng trnh (2) c 2 nghim tha mn .t . Phng trnh Phng trnh m lgarit Do nn khng tn ti TH2. Phng trnh (2) c 2 nghim . bi . tha mn hoc Cho phng trnh Xc nh tham s (1) phng trnh (1) c 2 nghim tha mn Bin i tng phng trnh cho v dng tng ng: Ta c : (3) Ta nhn thy phng trnh (3) c hai nghim l : v ,ta c : By gi ta kim tra iu kin (1): T PT (3) hoc .Do BPT (1) tr thnh (5) vo (5) ta c a) Thay (6) vo (5) ta c : b)Thay (7) Kt hp bt ng thc ta (4),(6),(7) thu c kt qu: hoc . bi Gii h phng trnh: H phng trnh hoc bi (4) Phng trnh m lgarit Cho phng trnh : (1) ( m l tham s ) . Tm m phng trnh (1) c t nht mt nghim thuc (2) iu kin . t . Ta c : (3) . Vy (2) c nghim t khi v ch khi (3) c nghim . . Cch 1 : Hm s Ta c : l hm tng trn on . Phng trnh . c nghim . . Cch 2 : Trng hp 1 : Phng trnh (3) c 2 nghim tha mn nn khng tn ti m. Do Trng hp 2 : Phng trnh (3) c 2 nghim tha mn h o c bi Gii phng trnh : Bi gii ca bn: vtduc1990 21:14:51 Ngy 10-01-2008 iu kin:-6<x<4 v x khc -2 . Phng trnh m lgarit bi Gii bt phng trnh : Bi gii chi tit | Vit cch gii khc ca bn Gii ra ta c bi Gii phng trnh Bi gii chi tit | Vit cch gii khc ca bn C Phng trnh k: *) *) tha mn iu kin p s: bi Gii bt phng trnh Bi gii chi tit | Vit cch gii khc ca Phng trnh m lgarit bn Vit li phng trnh thnh: t ta c bi Cho bt phng trnh: Tm . bt phng tnh c nghim ng vi mi Bi gii chi tit | Vit cch gii khc ca bn tha mn iu kin (1) t lun cng du vi ly cc gi tr trong khong . (2) (1) ng ng p s: . bi Gii phng trnh: Bi gii chi tit | Vit cch gii khc ca bn Phng trnh tng ng vi: R rng phng trnh c l nghim Ta c vi ; Suy ra l hm lin tc,ng bin v nhn c gi tr m,c gi tr dng trn R nn phng trnh c nghim duy nht . T bng bin thin ca hm Vy phng trnh c ng hai nghim : c khng qu hai nghim. . Ch : * C th chng minh phng trnh c nghim nh sau : Ta c : Suy ra phng trnh c nghim * C th s dng nh l Lagrange chng minh . c nghim bi Tm mi tha mn bt phng trnh Bi gii chi tit | Vit cch gii khc ca . Phng trnh m lgarit bn iu kin .Bt phng trnh c th vit di dng . t . Khi bt phng trnh tr thnh Kt hp ta c Bt phng trnh ng khi v ch khi bi Gii phng trnh . Bi gii chi tit | Vit cch gii khc ca bn iu kin c ngha: t R rng . l nghim ca (*). Li c . V tri l hm nghch bin, v phi l hm ng bin, vy nghim duy nht ca phng trnh p s : . l nghim duy nht ca (*) l

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