Sr Examen
Otras calculadoras
- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
- x^2+64>=0
-
(x+3)*(x-0,5)<0
-
5(x+2)-2(3x-1)>4x
-
17+12x<9x-4
-
Expresiones idénticas
- log(cuatro)^x+ dos < dos
- logaritmo de (4) en el grado x más 2 menos 2
- logaritmo de (cuatro) en el grado x más dos menos dos
- log(4)x+2<2
- log4x+2<2
- log4^x+2<2
-
Expresiones semejantes
- log(4)^x-2<2
-
Expresiones con funciones
- Logaritmo log
- log(x)^2>0
- log_5(x)<=-1
- log56*log6(x+10)>log5(8-x)
- log5(-15+7x)>3
- log4x<1
log(4)^x+2<2 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\log{\left(4 \right)}^{x} + 2 < 2$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\log{\left(4 \right)}^{x} + 2 = 2$$
Resolvemos:
$$x_{1} = -102.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{3} = -92.2059094953824$$
$$x_{4} = -162.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{9} = -96.2059094953824$$
$$x_{10} = -112.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{12} = -94.2059094953824$$
$$x_{13} = -158.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{15} = -84.2059094953824$$
$$x_{16} = -152.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{28} = -164.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{31} = -90.2059094953824$$
$$x_{32} = -126.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{35} = -148.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{39} = -86.2059094953824$$
$$x_{40} = -142.205909495382$$
$$x_{41} = -134.205909495382$$
$$x_{1} = -102.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{3} = -92.2059094953824$$
$$x_{4} = -162.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{9} = -96.2059094953824$$
$$x_{10} = -112.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{12} = -94.2059094953824$$
$$x_{13} = -158.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{15} = -84.2059094953824$$
$$x_{16} = -152.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{28} = -164.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{31} = -90.2059094953824$$
$$x_{32} = -126.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{35} = -148.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{39} = -86.2059094953824$$
$$x_{40} = -142.205909495382$$
$$x_{41} = -134.205909495382$$
Las raíces dadas
$$x_{28} = -164.205909495382$$
$$x_{4} = -162.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{13} = -158.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{16} = -152.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{35} = -148.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{40} = -142.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{41} = -134.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{32} = -126.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{10} = -112.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{1} = -102.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{9} = -96.2059094953824$$
$$x_{12} = -94.2059094953824$$
$$x_{3} = -92.2059094953824$$
$$x_{31} = -90.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{39} = -86.2059094953824$$
$$x_{15} = -84.2059094953824$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{28}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{28} - \frac{1}{10}$$
=
$$-164.205909495382 + - \frac{1}{10}$$
=
$$-164.305909495382$$
lo sustituimos en la expresión
$$\log{\left(4 \right)}^{x} + 2 < 2$$
$$\log{\left(4 \right)}^{-164.305909495382} + 2 < 2$$
pero
Entonces
$$x < -164.205909495382$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -164.205909495382 \wedge x < -162.205909495382$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -164.205909495382 \wedge x < -162.205909495382$$
$$x > -160.205909495382 \wedge x < -158.205909495382$$
$$x > -156.205909495382 \wedge x < -154.205909495382$$
$$x > -152.205909495382 \wedge x < -150.205909495382$$
$$x > -148.205909495382 \wedge x < -146.205909495382$$
$$x > -144.205909495382 \wedge x < -142.205909495382$$
$$x > -140.205909495382 \wedge x < -138.205909495382$$
$$x > -136.205909495382 \wedge x < -134.205909495382$$
$$x > -132.205909495382 \wedge x < -130.205909495382$$
$$x > -128.205909495382 \wedge x < -126.205909495382$$
$$x > -124.205909495382 \wedge x < -122.205909495382$$
$$x > -120.205909495382 \wedge x < -118.205909495382$$
$$x > -116.205909495382 \wedge x < -114.205909495382$$
$$x > -112.205909495382 \wedge x < -110.205909495382$$
$$x > -108.205909495382 \wedge x < -106.205909495382$$
$$x > -104.205909495382 \wedge x < -102.205909495382$$
$$x > -100.205909495382 \wedge x < -98.2059094953824$$
$$x > -96.2059094953824 \wedge x < -94.2059094953824$$
$$x > -92.2059094953824 \wedge x < -90.2059094953824$$
$$x > -88.2059094953824 \wedge x < -86.2059094953824$$
$$x > -84.2059094953824$$
$$\log{\left(4 \right)}^{x} + 2 < 2$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\log{\left(4 \right)}^{x} + 2 = 2$$
Resolvemos:
$$x_{1} = -102.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{3} = -92.2059094953824$$
$$x_{4} = -162.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{9} = -96.2059094953824$$
$$x_{10} = -112.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{12} = -94.2059094953824$$
$$x_{13} = -158.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{15} = -84.2059094953824$$
$$x_{16} = -152.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{28} = -164.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{31} = -90.2059094953824$$
$$x_{32} = -126.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{35} = -148.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{39} = -86.2059094953824$$
$$x_{40} = -142.205909495382$$
$$x_{41} = -134.205909495382$$
$$x_{1} = -102.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{3} = -92.2059094953824$$
$$x_{4} = -162.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{9} = -96.2059094953824$$
$$x_{10} = -112.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{12} = -94.2059094953824$$
$$x_{13} = -158.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{15} = -84.2059094953824$$
$$x_{16} = -152.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{28} = -164.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{31} = -90.2059094953824$$
$$x_{32} = -126.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{35} = -148.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{39} = -86.2059094953824$$
$$x_{40} = -142.205909495382$$
$$x_{41} = -134.205909495382$$
Las raíces dadas
$$x_{28} = -164.205909495382$$
$$x_{4} = -162.205909495382$$
$$x_{7} = -160.205909495382$$
$$x_{13} = -158.205909495382$$
$$x_{38} = -156.205909495382$$
$$x_{11} = -154.205909495382$$
$$x_{16} = -152.205909495382$$
$$x_{27} = -150.205909495382$$
$$x_{35} = -148.205909495382$$
$$x_{20} = -146.205909495382$$
$$x_{37} = -144.205909495382$$
$$x_{40} = -142.205909495382$$
$$x_{22} = -140.205909495382$$
$$x_{2} = -138.205909495382$$
$$x_{5} = -136.205909495382$$
$$x_{41} = -134.205909495382$$
$$x_{8} = -132.205909495382$$
$$x_{30} = -130.205909495382$$
$$x_{26} = -128.205909495382$$
$$x_{32} = -126.205909495382$$
$$x_{14} = -124.205909495382$$
$$x_{6} = -122.205909495382$$
$$x_{25} = -120.205909495382$$
$$x_{17} = -118.205909495382$$
$$x_{18} = -116.205909495382$$
$$x_{23} = -114.205909495382$$
$$x_{10} = -112.205909495382$$
$$x_{36} = -110.205909495382$$
$$x_{19} = -108.205909495382$$
$$x_{21} = -106.205909495382$$
$$x_{29} = -104.205909495382$$
$$x_{1} = -102.205909495382$$
$$x_{24} = -100.205909495382$$
$$x_{33} = -98.2059094953824$$
$$x_{9} = -96.2059094953824$$
$$x_{12} = -94.2059094953824$$
$$x_{3} = -92.2059094953824$$
$$x_{31} = -90.2059094953824$$
$$x_{34} = -88.2059094953824$$
$$x_{39} = -86.2059094953824$$
$$x_{15} = -84.2059094953824$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{28}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{28} - \frac{1}{10}$$
=
$$-164.205909495382 + - \frac{1}{10}$$
=
$$-164.305909495382$$
lo sustituimos en la expresión
$$\log{\left(4 \right)}^{x} + 2 < 2$$
$$\log{\left(4 \right)}^{-164.305909495382} + 2 < 2$$
-164.305909495382
2 + log (4) < 2
pero
-164.305909495382
2 + log (4) > 2
Entonces
$$x < -164.205909495382$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -164.205909495382 \wedge x < -162.205909495382$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x28 x4 x7 x13 x38 x11 x16 x27 x35 x20 x37 x40 x22 x2 x5 x41 x8 x30 x26 x32 x14 x6 x25 x17 x18 x23 x10 x36 x19 x21 x29 x1 x24 x33 x9 x12 x3 x31 x34 x39 x15Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -164.205909495382 \wedge x < -162.205909495382$$
$$x > -160.205909495382 \wedge x < -158.205909495382$$
$$x > -156.205909495382 \wedge x < -154.205909495382$$
$$x > -152.205909495382 \wedge x < -150.205909495382$$
$$x > -148.205909495382 \wedge x < -146.205909495382$$
$$x > -144.205909495382 \wedge x < -142.205909495382$$
$$x > -140.205909495382 \wedge x < -138.205909495382$$
$$x > -136.205909495382 \wedge x < -134.205909495382$$
$$x > -132.205909495382 \wedge x < -130.205909495382$$
$$x > -128.205909495382 \wedge x < -126.205909495382$$
$$x > -124.205909495382 \wedge x < -122.205909495382$$
$$x > -120.205909495382 \wedge x < -118.205909495382$$
$$x > -116.205909495382 \wedge x < -114.205909495382$$
$$x > -112.205909495382 \wedge x < -110.205909495382$$
$$x > -108.205909495382 \wedge x < -106.205909495382$$
$$x > -104.205909495382 \wedge x < -102.205909495382$$
$$x > -100.205909495382 \wedge x < -98.2059094953824$$
$$x > -96.2059094953824 \wedge x < -94.2059094953824$$
$$x > -92.2059094953824 \wedge x < -90.2059094953824$$
$$x > -88.2059094953824 \wedge x < -86.2059094953824$$
$$x > -84.2059094953824$$
Solución de la desigualdad en el gráfico
Respuesta rápida
Esta desigualdad no tiene soluciones