Bai tap PT he PT logarit

<span class='text_page_counter'>(1)</span>Chuyên đề PT, BPT Mũ – Lôgarit. . LuyÖn TËp Ph−¬ng Tr×nh, HÖ Ph−¬ng Tr×nh L«garit Bài 1Giải phương trình: 22) 2. log 2 x + log 2 16 x − 7 = 0 23) log 3 (3x − 1) log 3 (3x +1 − 3) = 6. 1 2 + =1 4 − lg x 2 + lg x 2) log 2 16 + log2x 64 = 3 x 1). 24) log 4 log 2 x + log 2 log 4 x = 2. log 0,04 x + 1 + log 0,2 x + 3 = 1. 3). 25) log x 3 + log 3 x = log. 4) log 2 x + 10 log 2 x + 6 = 0. 26). 5) 3log x 16 − 4 log16 x = 2 log 2 x. (. ). (. (. 7) lg 6.5 + 25.20 x. (. 8) x + lg 4 − 5. x. x. x. ). ) = x + lg 25. 1 2 + =1 4 − lg x 2 + lg x. (. ) = x lg 2 + lg3. ). 2. 30) log5 x + log25 x = log 0,2 3. lg x. 31) lg(x + 2x − 3) + lg 2. 32). log ( x +3 ) 12) 2 5 =x 13) log 4 log 2 x + log 2 log 4 x = 2. 14) log x 3 + log 3 x = log. x. 3 + log 3. x+3 =0 x −1. 1 .lg(5x − 4) + lg x + 1 = 2 + lg 0,18 2. 33) 3log x 16 − 4 log16 x = 2 log 2 x. 1 x + 2. 34) lg(lg x) + lg(lg x − 2) = 0 3. (. 2. ). (. ). 15) log x (125x) . log 25 x = 1. 35) log 2 4.3 − 6 − log 2 9 − 6 = 1. 17) log 22 x + 2 log 2. 36) log3  log9 x +. 16) (x − 1) log 2 [4( x −1) ] = 8 (x − 1) 3. 18) 2.2. (. x− 2. ). 2. x. x. 1   + 9 x  = 2x 2   x x 37) lg 6.5 + 25.20 = x + lg25. x −2=0. (. = log 2 ( 2x ). 19) x = x .3log2 x − x log2 3 20) 1 + log 2 ( x − 1) = log x −1 4 log 2 9. 2. 38) 3. log32 x. ). + x log3 x = 162. 21) lg 2 x − 5 lg x = lg x 3 − 7 39) log 2 (x − x 2 − 1) log 3 (x + x 2 − 1) = log 6 x − x 2 − 1 log 3 (3x − 1) log 3 (3x +1 − 3) = 6. (. 40) log2 4. x +1. (. ). + 4 .log 2 4 x + 1 = log. 41) ( x + 2 ) log3 42) log 3 (sin. ). 2. 1 2. 1 8. ( x + 1) + 4 ( x + 1) log3 ( x + 1) − 16 = 0. x x − sin x) + log 1 (sin + cos 2x) = 0. (Đề 3) 2 2 3. 43) log 2 (x − x 2 − 1) log 3 (x + x 2 − 1) = log 6 x − x 2 − 1. Gi¸o viªn: Th©n V¨n Dù. 1 2. 29) log x 2x − 5x + 4 = 2. = 50 − x lg5 log 2 x log x 10) 3 3 + x 3 = 162 11) log3 ( x + 1) + log5 ( 2x + 1) = 2. 9) 5. 3 + log 3 x +. 27) 2 log 5 ( x + 3) = x. 28) log5 x = log5 ( x + 6 ) − log5 ( x + 2 ). 6) log 2 4.3 − 6 − log 2 9 − 6 = 1 x. x. §T: 0984 214 648.

<span class='text_page_counter'>(2)</span> Chuyên đề PT, BPT Mũ – Lôgarit. . Bài 2 Cho phương trình: (m – 3) log 21 (x − 4) – (2m + 1) log 1 (x − 4) + m + 2 = 0 2. 2. tìm m để phương trình có 2 nghiệm x1, x 2 thoả mãn 4 < x1 Bài 3 Giải các hệ phương trình sau:  x − 1 + 2 − y = 1 5) 1)  2 3 3log (9x ) − log y = 3  9 3 1 x−2 y  x− y 6) ( 3 ) = ( ) 2)  3 log 2 ( x − y ) + log 2 ( x − y ) = 4 7) 1  log 1 ( y − x) − log 4 y = 1 3)  4  x 2 + y 2 = 25 8) .  3 4−x ( x + 1 − 1)3y = 4)  x y + log x = 1  3. < x2 < 6.  x log8 y + y log8 x = 4  log 4 x − log 4 y = 1. x − 4 y + 3 = 0   log 4 x − log2 y = 0 log 2 ( x 2 + y 2 ) = 5  2 log 4 x + log 2 y = 4 log x y + log y x = 2  2  x − 3 x − y = 20 + log y x. Bài 4 Giải hệ phương trình. lg x + lg y = 1 1)  2 2 x + y = 29 lg x 2 + y 2 = 1 + 3lg2 2)  lg ( x + y ) − lg ( x − y ) = lg3 log 4 x − log 2 y = 0 3)  2 2 x − 5y + 4 = 0. (. ). Gi¸o viªn: Th©n V¨n Dù.  x+y  y x = 32 4)  4 log3 ( x + y ) = 1 − log3 ( x + y ) log x xy = log y x 2 5)  2 log x y y = 4y + 3 3 − x .2 y = 1152 6)  log 5 ( x + y ) = 2. §T: 0984 214 648.

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