Bất phương trình \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaisdaaeqaaOWaaeWabeaacaWG4bGaey4k % aSIaaG4naaGaayjkaiaawMcaaiabg6da+iGacYgacaGGVbGaai4zam % aaBaaaleaacaaIYaaabeaakmaabmqabaGaamiEaiabgUcaRiaaigda % aiaawIcacaGLPaaaaaa!46CF! {\log _4}\left( {x + 7} \right) > {\log _2}\left( {x + 1} \right)\) có bao nhiêu nghiệm nguyên?

Điều kiện:  x > -1(*)

Khi đó:\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciiBaiaac+ % gacaGGNbWaaSbaaSqaaiaaisdaaeqaaOWaaeWaaeaacaWG4bGaey4k % aSIaaG4naaGaayjkaiaawMcaaiabg6da+iGacYgacaGGVbGaai4zam % aaBaaaleaacaaIYaaabeaakmaabmaabaGaamiEaiabgUcaRiaaigda % aiaawIcacaGLPaaacqGHuhY2daWcaaqaaiaaigdaaeaacaaIYaaaai % GacYgacaGGVbGaai4zamaaBaaaleaacaaIYaaabeaakmaabmaabaGa % amiEaiabgUcaRiaaiEdaaiaawIcacaGLPaaacqGH+aGpciGGSbGaai % 4BaiaacEgadaWgaaWcbaGaaGOmaaqabaGcdaqadaqaaiaadIhacqGH % RaWkcaaIXaaacaGLOaGaayzkaaGaeyi1HSTaciiBaiaac+gacaGGNb % WaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaWG4bGaey4kaSIaaG4n % aaGaayjkaiaawMcaaiabg6da+iGacYgacaGGVbGaai4zamaaBaaale % aacaaIYaaabeaakmaabmaabaGaamiEaiabgUcaRiaaigdaaiaawIca % caGLPaaadaahaaWcbeqaaiaaikdaaaaaaa!6FA6! {\log _4}\left( {x + 7} \right) > {\log _2}\left( {x + 1} \right) \Leftrightarrow \frac{1}{2}{\log _2}\left( {x + 7} \right) > {\log _2}\left( {x + 1} \right) \Leftrightarrow {\log _2}\left( {x + 7} \right) > {\log _2}{\left( {x + 1} \right)^2}\)

\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyi1HSTaam % iEaiabgUcaRiaaiEdacqGH+aGpcaWG4bWaaWbaaSqabeaacaaIYaaa % aOGaey4kaSIaaGOmaiaadIhacqGHRaWkcaaIXaGaeyi1HSTaamiEam % aaCaaaleqabaGaaGOmaaaakiabgUcaRiaadIhacqGHsislcaaI2aGa % eyipaWJaaGimaiabgsDiBlabgkHiTiaaiodacqGH8aapcaWG4bGaey % ipaWJaaGOmaaaa!537D! \Leftrightarrow x + 7 > {x^2} + 2x + 1 \Leftrightarrow {x^2} + x - 6 < 0 \Leftrightarrow - 3 < x < 2\)

Kết hợp với (*) ta có nghiệm là -1 < x < 2

Do \(x \in Z\) nên \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabg2 % da9iaaicdacqGHOiI2caWG4bGaeyypa0JaaGymaaaa!3D1F! x = 0 \vee x = 1\)