Tập nghiệm của bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaamaalaaabaGaaGymaaqaaiaaikdaaaaabeaa % kmaabmaabaGaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaO % WaaeWaaeaacaaIYaGaamiEaiabgkHiTiaaigdaaiaawIcacaGLPaaa % aiaawIcacaGLPaaacqGH+aGpcaaIWaaaaa!4678! {\log _{\frac{1}{2}}}\left( {{{\log }_2}\left( {2x - 1} \right)} \right) > 0\) là:

Điều kiện \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe % qaaiaaikdacaWG4bGaeyOeI0IaaGymaiabg6da+iaaicdaaeaaciGG % SbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGccaGGOaGaaGOmai % aadIhacqGHsislcaaIXaGaaiykaiabg6da+iaaicdaaaGaay5EaaGa % eyi1HSTaamiEaiabg6da+iaaigdacaGGUaaaaa!4C44! \left\{ \begin{array}{l} 2x - 1 > 0\\ {\log _2}(2x - 1) > 0 \end{array} \right. \Leftrightarrow x > 1.\)

Ta có : \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaamaalaaabaGaaGymaaqaaiaaikdaaaaabeaa % kmaabmaabaGaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaO % WaaeWaaeaacaaIYaGaamiEaiabgkHiTiaaigdaaiaawIcacaGLPaaa % aiaawIcacaGLPaaacqGH+aGpcaaIWaGaeyi1HSTaciiBaiaac+gaca % GGNbWaaSbaaSqaamaalaaabaGaaGymaaqaaiaaikdaaaaabeaakmaa % bmaabaGaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaae % WaaeaacaaIYaGaamiEaiabgkHiTiaaigdaaiaawIcacaGLPaaaaiaa % wIcacaGLPaaacqGH+aGpciGGSbGaai4BaiaacEgadaWgaaWcbaWaaS % aaaeaacaaIXaaabaGaaGOmaaaaaeqaaOGaaGymaaaa!5DE6! {\log _{\frac{1}{2}}}\left( {{{\log }_2}\left( {2x - 1} \right)} \right) > 0 \Leftrightarrow {\log _{\frac{1}{2}}}\left( {{{\log }_2}\left( {2x - 1} \right)} \right) > {\log _{\frac{1}{2}}}1\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaa % kiaacIcacaaIYaGaamiEaiabgkHiTiaaigdacaGGPaGaeyipaWJaaG % ymaaqaaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaakiaa % cIcacaaIYaGaamiEaiabgkHiTiaaigdacaGGPaGaeyOpa4JaaGimaa % aacaGL7baacqGHuhY2daGabaabaeqabaGaaGimaiabgYda8iaaikda % caWG4bGaeyOeI0IaaGymaiabgYda8iaaikdaaeaacaaIYaGaamiEai % abgkHiTiaaigdacqGH+aGpcaaIXaaaaiaawUhaaiabgsDiBlaaigda % cqGH8aapcaWG4bGaeyipaWZaaSaaaeaacaaIZaaabaGaaGOmaaaaca % GGUaaaaa!65C1! \Leftrightarrow \left\{ \begin{array}{l} {\log _2}(2x - 1) < 1\\ {\log _2}(2x - 1) > 0 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 0 < 2x - 1 < 2\\ 2x - 1 > 1 \end{array} \right. \Leftrightarrow 1 < x < \frac{3}{2}.\) ( thỏa mãn điều kiện)

Vậy tập nghiệm của bất phương trình đã cho là \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiabg2 % da9maabmaabaGaaGymaiaacUdadaWcaaqaaiaaiodaaeaacaaIYaaa % aaGaayjkaiaawMcaaaaa!3C5E! S = \left( {1;\frac{3}{2}} \right)\)