Nghiệm nguyên nhỏ nhất của bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaaciGGSbGaai4B % aiaacEgadaWgaaWcbaGaaGinaaqabaGccaWG4baacaGLOaGaayzkaa % GaeyyzImRaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaisdaaeqaaOWa % aeWaaeaaciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGcca % WG4baacaGLOaGaayzkaaaaaa!4BD2! {\log _2}\left( {{{\log }_4}x} \right) \ge {\log _4}\left( {{{\log }_2}x} \right)\) là:

BPT\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaadIhacqGH+aGpcaaIWaaabaGaciiBaiaac+gacaGG % NbWaaSbaaSqaaiaaikdaaeqaaOGaamiEaiabg6da+iaaicdaaeaaci % GGSbGaai4BaiaacEgadaWgaaWcbaGaaGinaaqabaGccaWG4bGaeyOp % a4JaaGimaaqaaiabgUcaRiGacYgacaGGVbGaai4zamaaBaaaleaaca % aIYaaabeaakmaabmaabaGaciiBaiaac+gacaGGNbWaaSbaaSqaaiaa % ikdadaahaaadbeqaaiaaikdaaaaaleqaaOGaamiEaaGaayjkaiaawM % caaiabgwMiZkGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaWaaWba % aWqabeaacaaIYaaaaaWcbeaakmaabmaabaGaciiBaiaac+gacaGGNb % WaaSbaaSqaaiaaikdaaeqaaOGaamiEaaGaayjkaiaawMcaaaaacaGL % 7baacqGHuhY2daGabaabaeqabaGaamiEaiabg6da+iaaigdaaeaacq % GHRaWkciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGcdaqa % daqaamaalaaabaGaaGymaaqaaiaaikdaaaGaciiBaiaac+gacaGGNb % WaaSbaaSqaaiaaikdaaeqaaOGaamiEaaGaayjkaiaawMcaaiabgwMi % ZoaalaaabaGaaGymaaqaaiaaikdaaaGaciiBaiaac+gacaGGNbWaaS % baaSqaaiaaikdaaeqaaOWaaeWaaeaaciGGSbGaai4BaiaacEgadaWg % aaWcbaGaaGOmaaqabaGccaWG4baacaGLOaGaayzkaaaaaiaawUhaaa % aa!81E2! \Leftrightarrow \left\{ \begin{array}{l} x > 0\\ {\log _2}x > 0\\ {\log _4}x > 0\\ + {\log _2}\left( {{{\log }_{{2^2}}}x} \right) \ge {\log _{{2^2}}}\left( {{{\log }_2}x} \right) \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x > 1\\ + {\log _2}\left( {\frac{1}{2}{{\log }_2}x} \right) \ge \frac{1}{2}{\log _2}\left( {{{\log }_2}x} \right) \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaadIhacqGH+aGpcaaIXaaabaGaey4kaSIaciiBaiaa % c+gacaGGNbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaadaWcaaqaai % aaigdaaeaacaaIYaaaaiGacYgacaGGVbGaai4zamaaBaaaleaacaaI % YaaabeaakiaadIhaaiaawIcacaGLPaaacqGHLjYSdaWcaaqaaiaaig % daaeaacaaIYaaaaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaa % beaakmaabmaabaGaciiBaiaac+gacaGGNbWaaSbaaSqaaiaaikdaae % qaaOGaamiEaaGaayjkaiaawMcaaaaacaGL7baacqGHuhY2daGabaab % aeqabaGaamiEaiabg6da+iaaigdaaeaaciGGSbGaai4BaiaacEgada % WgaaWcbaGaaGOmaaqabaGcdaqadaqaaiGacYgacaGGVbGaai4zamaa % BaaaleaacaaIYaaabeaakiaadIhaaiaawIcacaGLPaaacqGHsislca % aIXaGaeyyzIm7aaSaaaeaacaaIXaaabaGaaGOmaaaaciGGSbGaai4B % aiaacEgadaWgaaWcbaGaaGOmaaqabaGcdaqadaqaaiGacYgacaGGVb % Gaai4zamaaBaaaleaacaaIYaaabeaakiaadIhaaiaawIcacaGLPaaa % aaGaay5Eaaaaaa!7540! \Leftrightarrow \left\{ \begin{array}{l} x > 1\\ + {\log _2}\left( {\frac{1}{2}{{\log }_2}x} \right) \ge \frac{1}{2}{\log _2}\left( {{{\log }_2}x} \right) \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x > 1\\ {\log _2}\left( {{{\log }_2}x} \right) - 1 \ge \frac{1}{2}{\log _2}\left( {{{\log }_2}x} \right) \end{array} \right.\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaadIhacqGH+aGpcaaIXaaabaWaaSaaaeaacaaIXaaa % baGaaGOmaaaaciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqaba % GcdaqadaqaaiGacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaa % kiaadIhaaiaawIcacaGLPaaacqGHLjYScaaIXaaaaiaawUhaaaaa!4A42! \Leftrightarrow \left\{ \begin{array}{l} x > 1\\ \frac{1}{2}{\log _2}\left( {{{\log }_2}x} \right) \ge 1 \end{array} \right.\)\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HS9aai % qaaqaabeqaaiaadIhacqGH+aGpcaaIXaaabaGaciiBaiaac+gacaGG % NbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaaciGGSbGaai4BaiaacE % gadaWgaaWcbaGaaGOmaaqabaGccaWG4baacaGLOaGaayzkaaGaeyyz % ImRaaGOmaaaacaGL7baacqGHshI3daGabaabaeqabaGaamiEaiabg6 % da+iaaigdaaeaaciGGSbGaai4BaiaacEgadaWgaaWcbaGaaGOmaaqa % baGccaWG4bGaeyyzImRaaGinaaaacaGL7baacqGHshI3daGabaabae % qabaGaamiEaiabg6da+iaaigdaaeaacaWG4bGaeyyzImRaaGioaaaa % caGL7baacqGHshI3caWG4bGaeyyzImRaaGioaaaa!65E2! \Leftrightarrow \left\{ \begin{array}{l} x > 1\\ {\log _2}\left( {{{\log }_2}x} \right) \ge 2 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x > 1\\ {\log _2}x \ge 4 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} x > 1\\ x \ge 8 \end{array} \right. \Rightarrow x \ge 8\)