Logarifmik tenglamalar

Agzamxo'djayeva M.SH Mavzu:Logarifmik tenglamalar. Logarifm xossalari log (bc)  log b  log c a a a b log b  log c log  a a a c r log b  r log b a a 1 log b  log b ar r a log b log b  c a log a c Ifodalar qiymatlarini hisoblang: log 16  log 4 log 33  log 11 8 8 3 3 lg 25  lg 4 lg 34  lg 3,4 log log 27 log log 16 3 3 2 2 log 49 log 64 5 3 log 7 log 4 5 3 Ta'rif: Noma'lumli logarifm belgisi ostida qatnashgan tenglama logarifmik tenglama deyiladi. log f (x)  b a log b  a f(x) log x = b (a 0, a ≠ 1) tenglamani qaraymiz. Bu tenglama eng a b sodda logarifmik tenglama deyiladi. x = a son qaralayotgan tenglamaning ildizi bo'lishini ko'rish qiyin emas. b Berilgan tenglama x = a dan boshqa ildizga ega emasligini y = log x logarifmik funksiyaning monotonligidan foydalanib a isbotlash mumkin LT yechish usullari: Tenglamani turi log f (x)  b 1. Logarifm ta'rifini qo'llashga a doir 2. Yangi o'zgaruvchini kiritish log2 f (x)blog f (x)c  0 usuli a a 3. Bitta asosga keltirish usuli log f (x)  log g(x) 4. Potensilashtirish usuli a a 5. Tenglamaning ikkala tomonini logarifmlash usuli 6. Funksional-grafik uslubi log f (x)  g(x) a log2 x  5log x  6  0 1- misol 3 3 Aniqlanish sohasi : x  0 Belgilaymiz log x  t 3 t2  5t  6  0 t  3,t  2 1 2 1)log x  3 3 x  33  27 2)log x  2 3 x  32  9 Javob :9;27. 2- misol 3- misol log (3x  4)  log (5x 8) 7 7   log 3x  5  4 3x  4  5x 8 2 3x  5  24 3x 5x  8 4  2x  4 3x 16  5 x  2 3x  21 Tekshirish : x  2da x  7 tenglamaning chap va o'ng tomonlari ma'noga ega emas. Javob: yechimi yoq xlog 3 x1  9; 5- misol 4- misol Aniqlanish sohasi : x  0, x  1 Logariflaymiz log x 2log x ...