Biết \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9maalaaabaGaaGymaiaaiwdaaeaacaaIYaaaaaaa!3A3D! x = \frac{{15}}{2}\) là một nghiệm của bất phương trình   \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiGacY % gacaGGVbGaai4zamaaBaaaleaacaWGHbaabeaakmaabmaabaGaaGOm % aiaaiodacaWG4bGaeyOeI0IaaGOmaiaaiodaaiaawIcacaGLPaaacq % GH+aGpciGGSbGaai4BaiaacEgadaWgaaWcbaWaaOaaaeaacaWGHbaa % meqaaaWcbeaakmaabmaabaGaamiEamaaCaaaleqabaGaaGOmaaaaki % abgUcaRiaaikdacaWG4bGaey4kaSIaaGymaiaaiwdaaiaawIcacaGL % Paaaaaa!4E8C! 2{\log _a}\left( {23x - 23} \right) > {\log _{\sqrt a }}\left( {{x^2} + 2x + 15} \right)\) (*). Tập nghiệm T của bất phương trình (*) là

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiGacY % gacaGGVbGaai4zamaaBaaaleaacaWGHbaabeaakmaabmaabaGaaGOm % aiaaiodacaWG4bGaeyOeI0IaaGOmaiaaiodaaiaawIcacaGLPaaacq % GH+aGpciGGSbGaai4BaiaacEgadaWgaaWcbaWaaOaaaeaacaWGHbaa % meqaaaWcbeaakmaabmaabaGaamiEamaaCaaaleqabaGaaGOmaaaaki % abgUcaRiaaikdacaWG4bGaey4kaSIaaGymaiaaiwdaaiaawIcacaGL % PaaacqGHuhY2ciGGSbGaai4BaiaacEgadaWgaaWcbaGaamyyaaqaba % GcdaqadaqaaiaaikdacaaIZaGaamiEaiabgkHiTiaaikdacaaIZaaa % caGLOaGaayzkaaGaeyOpa4JaciiBaiaac+gacaGGNbWaaSbaaSqaai % aadggaaeqaaOWaaeWaaeaacaWG4bWaaWbaaSqabeaacaaIYaaaaOGa % ey4kaSIaaGOmaiaadIhacqGHRaWkcaaIXaGaaGynaaGaayjkaiaawM % caaaaa!689D! 2{\log _a}\left( {23x - 23} \right) > {\log _{\sqrt a }}\left( {{x^2} + 2x + 15} \right) \Leftrightarrow {\log _a}\left( {23x - 23} \right) > {\log _a}\left( {{x^2} + 2x + 15} \right)\)

Nếu a > 1  ta có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaadggaaeqaaOWaaeWaaeaacaaIYaGaaG4m % aiaadIhacqGHsislcaaIYaGaaG4maaGaayjkaiaawMcaaiabg6da+i % GacYgacaGGVbGaai4zamaaBaaaleaacaWGHbaabeaakmaabmaabaGa % amiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaikdacaWG4bGaey % 4kaSIaaGymaiaaiwdaaiaawIcacaGLPaaacqGHuhY2daGabaabaeqa % baGaaGOmaiaaiodacaWG4bGaeyOeI0IaaGOmaiaaiodacqGH+aGpca % WG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGOmaiaadIhacqGH % RaWkcaaIXaGaaGynaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccq % GHRaWkcaaIYaGaamiEaiabgUcaRiaaigdacaaI1aGaeyOpa4JaaGim % aaaacaGL7baacqGHuhY2caaIYaGaeyipaWJaamiEaiabgYda8iaaig % dacaaI5aaaaa!6E35! {\log _a}\left( {23x - 23} \right) > {\log _a}\left( {{x^2} + 2x + 15} \right) \Leftrightarrow \left\{ \begin{array}{l} 23x - 23 > {x^2} + 2x + 15\\ {x^2} + 2x + 15 > 0 \end{array} \right. \Leftrightarrow 2 < x < 19\)

Nếu 0 < a < 1 ta có \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaadggaaeqaaOWaaeWaaeaacaaIYaGaaG4m % aiaadIhacqGHsislcaaIYaGaaG4maaGaayjkaiaawMcaaiabg6da+i % GacYgacaGGVbGaai4zamaaBaaaleaacaWGHbaabeaakmaabmaabaGa % amiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaaikdacaWG4bGaey % 4kaSIaaGymaiaaiwdaaiaawIcacaGLPaaacqGHuhY2daGabaabaeqa % baGaaGOmaiaaiodacaWG4bGaeyOeI0IaaGOmaiaaiodacqGH8aapca % WG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGOmaiaadIhacqGH % RaWkcaaIXaGaaGynaaqaaiaaikdacaaIZaGaamiEaiabgkHiTiaaik % dacaaIZaGaeyOpa4JaaGimaaaacaGL7baacqGHuhY2daWabaabaeqa % baGaaGymaiabgYda8iaadIhacqGH8aapcaaIYaaabaGaamiEaiabg6 % da+iaaigdacaaI5aaaaiaawUfaaaaa!6FE8! {\log _a}\left( {23x - 23} \right) > {\log _a}\left( {{x^2} + 2x + 15} \right) \Leftrightarrow \left\{ \begin{array}{l} 23x - 23 < {x^2} + 2x + 15\\ 23x - 23 > 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} 1 < x < 2\\ x > 19 \end{array} \right.\)Mà \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9maalaaabaGaaGymaiaaiwdaaeaacaaIYaaaaaaa!3A3D! x = \frac{{15}}{2}\) là một nghiệm của bất phương trình.