Chuyen de mu va logarit_moi - Chuyen e 5: PHNG TRNH VA BAT...

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Chuyeân ñeà 5 : PHÖÔNG TRÌNH VAØ BAÁT PHÖÔNG COÙ CHÖÙA MUÕ VAØ LOGARÍT TOÙM TAÉT GIAÙO KHOA I. KIEÁN THÖÙC CÔ BAÛN VEÀ HAØM SOÁ MU Õ 1. Caùc ñònh nghóa : n n thua so a a.a. ..a = ±²³ (n Z ,n 1,a R) + ∈≥ 1 aa = a 0 a1 = a0 ∀≠ n n 1 a a = { } R / 0 ) + m n m n = ( ) ; m , nN >∈ m n m n m n 11 a a a == 20 2. Caùc tính chaát : mn a. a a + = m n a a a = nm m .n (a ) (a ) a nn n (a.b) a .b = n n n () b b =
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3. Haøm soá muõ : Daïng : ( a > 0 , a x ya = 1 ) Taäp xaùc ñònh : DR = Taäp giaù trò : ( ) TR + = x a0 x >∀ R Tính ñôn ñieäu: * a > 1 : ñoàng bieán treân x = R * 0 < a < 1 : nghòch bieán treân x = R Ñoà thò haøm soá muõ : a>1 y=a x y x 1 0<a<1 y=a x y x 1 Minh hoïa : f(x)=2^x -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 x y f(x)=(1/2)^x -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 x y y=2 x y= x 2 1 1 x y y x 1 O O 21
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II. KIEÁN THÖÙC CÔ BAÛN VEÀ HAØM SOÁ LOÂGARÍT 1. Ñònh nghóa : Vôùi a > 0 , a 1 vaø N > 0 dn M a log N M a N = ⇔= Ñieàu kieän coù nghóa : coù nghóa khi N a log > > 0 1 0 N a a 22 2. Caùc tính chaát : a log 1 0 = a log a 1 = M a log a M = log N a aN = a12 a1 a2 log (N .N ) log N log N =+ 1 aa 1 a 2 2 N log ( ) log N log N N =− a log N .log N α a Ñaëc bieät : 2 log N 2.log N = 3. Coâng thöùc ñoåi cô soá : b log N log b.log N = a b a log N log N log b = * Heä qua û: vaø ka a 1 lo a b 1 log b log a = g N log N k =
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4. Haøm soá logarít : Daïng ( a > 0 , a a yl o gx = 1 ) Taäp xaùc ñònh : + = DR Taäp giaù trò = TR Tính ñôn ñieäu: * a > 1 : ñoàng bieán treân a o = + R * 0 < a < 1 : nghòch bieán treân a o = + R Ñoà thò cuûa haøm soá loâgarít: 0<a<1 y=log a x 1 x y O a>1 y=log a x 1 y x O Minh hoïa : f(x)=ln(x)/ln(1/2) -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 x y y=log 2 x x y x y f(x)=ln(x)/ln(2) -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 3.5 x y x y 2 1 log = 1 O 1 O 23
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5. CAÙC ÑÒNH LYÙ CÔ BAÛN : 1. Ñònh lyù 1 : Vôùi 0 < a 1 thì : a M = a N M = N 2. Ñònh lyù 2 : Vôùi 0 < a <1 thì : a M < a N M > N (nghòch bieán) 3. Ñònh lyù 3 : Vôùi a > 1 thì : a M < a N M < N (ñoàng bieán ) 4. Ñònh lyù 4 : Vôùi 0 < a 1 vaø M > 0;N > 0 thì : log a M = log a N M = N 5. Ñònh lyù 5 : Vôùi 0 < a <1 thì : log a M < log a N M >N (nghòch bieán) 6. Ñònh lyù 6 : Vôùi a > 1 thì : log a M < log a N M < N (ñoàng bieán) III. CAÙC PHÖÔNG PHAÙP GIAÛI PHÖÔNG TRÌNH MUÕ THÖÔØNG SÖÛ DUÏNG
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This note was uploaded on 06/15/2011 for the course METROPOLIT gep 101 taught by Professor Hakansukur during the Spring '10 term at Bahcesehir University.

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Chuyen de mu va logarit_moi - Chuyen e 5: PHNG TRNH VA BAT...

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