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-
¿Cómo usar?
- Desigualdades:
-
2^x>-1
- x^2+64<0
-
x^2<=6,5-9*(4-x)^2
-
(x+4)(x-1)>(x-7)(x+10)
-
Expresiones idénticas
- cuatro * nueve ^x- siete * doce ^x+ tres * dieciséis ^x> cero
- 4 multiplicar por 9 en el grado x menos 7 multiplicar por 12 en el grado x más 3 multiplicar por 16 en el grado x más 0
- cuatro multiplicar por nueve en el grado x menos siete multiplicar por doce en el grado x más tres multiplicar por dieciséis en el grado x más cero
- 4*9x-7*12x+3*16x>0
- 49^x-712^x+316^x>0
- 49x-712x+316x>0
-
Expresiones semejantes
- 4*9^x+7*12^x+3*16^x>0
- 4*9^x-7*12^x-3*16^x>0
4*9^x-7*12^x+3*16^x>0 desigualdades
Solución
Ha introducido
[src]
x x x 4*9 - 7*12 + 3*16 > 0
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
3*16^x - 7*12^x + 4*9^x > 0
Solución detallada
Se da la desigualdad:
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -75.4236742619834$$
$$x_{2} = -69.4236742836564$$
$$x_{3} = -21.4503302630093$$
$$x_{4} = 1$$
$$x_{5} = -79.4236742587756$$
$$x_{6} = -19.4717369349091$$
$$x_{7} = -49.4236825713738$$
$$x_{8} = -97.4236742572992$$
$$x_{9} = -29.4263005801687$$
$$x_{10} = -43.4237209724582$$
$$x_{11} = -51.4236789339511$$
$$x_{12} = -27.4283496621804$$
$$x_{13} = -107.423674257291$$
$$x_{14} = -89.4236742573745$$
$$x_{15} = -17.5113613217216$$
$$x_{16} = -35.4241410129855$$
$$x_{17} = -23.4385515501772$$
$$x_{18} = -85.4236742575551$$
$$x_{19} = -81.423674258126$$
$$x_{20} = -73.4236742656331$$
$$x_{21} = -47.4236890379465$$
$$x_{22} = -39.423821910242$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{25} = -99.4236742572956$$
$$x_{26} = -55.4236757370122$$
$$x_{27} = -63.4236744054299$$
$$x_{28} = -41.4237573084927$$
$$x_{29} = -45.4237005342138$$
$$x_{30} = -33.4245042464747$$
$$x_{31} = -77.4236742599304$$
$$x_{32} = -91.4236742573379$$
$$x_{33} = 0$$
$$x_{34} = -13.7446078221231$$
$$x_{35} = -83.4236742577606$$
$$x_{36} = -37.4239367715623$$
$$x_{37} = -61.4236745206493$$
$$x_{38} = -103.423674257292$$
$$x_{39} = -93.4236742573173$$
$$x_{40} = -105.423674257292$$
$$x_{41} = -31.425150430308$$
$$x_{42} = -87.4236742574395$$
$$x_{43} = -53.4236768879087$$
$$x_{44} = -25.4320063693618$$
$$x_{45} = -95.4236742573057$$
$$x_{46} = -101.423674257294$$
$$x_{47} = -67.423674304163$$
$$x_{48} = -71.4236742721215$$
$$x_{49} = -109.423674257291$$
$$x_{50} = -15.5873652307869$$
$$x_{51} = -65.4236743406191$$
$$x_{1} = -75.4236742619834$$
$$x_{2} = -69.4236742836564$$
$$x_{3} = -21.4503302630093$$
$$x_{4} = 1$$
$$x_{5} = -79.4236742587756$$
$$x_{6} = -19.4717369349091$$
$$x_{7} = -49.4236825713738$$
$$x_{8} = -97.4236742572992$$
$$x_{9} = -29.4263005801687$$
$$x_{10} = -43.4237209724582$$
$$x_{11} = -51.4236789339511$$
$$x_{12} = -27.4283496621804$$
$$x_{13} = -107.423674257291$$
$$x_{14} = -89.4236742573745$$
$$x_{15} = -17.5113613217216$$
$$x_{16} = -35.4241410129855$$
$$x_{17} = -23.4385515501772$$
$$x_{18} = -85.4236742575551$$
$$x_{19} = -81.423674258126$$
$$x_{20} = -73.4236742656331$$
$$x_{21} = -47.4236890379465$$
$$x_{22} = -39.423821910242$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{25} = -99.4236742572956$$
$$x_{26} = -55.4236757370122$$
$$x_{27} = -63.4236744054299$$
$$x_{28} = -41.4237573084927$$
$$x_{29} = -45.4237005342138$$
$$x_{30} = -33.4245042464747$$
$$x_{31} = -77.4236742599304$$
$$x_{32} = -91.4236742573379$$
$$x_{33} = 0$$
$$x_{34} = -13.7446078221231$$
$$x_{35} = -83.4236742577606$$
$$x_{36} = -37.4239367715623$$
$$x_{37} = -61.4236745206493$$
$$x_{38} = -103.423674257292$$
$$x_{39} = -93.4236742573173$$
$$x_{40} = -105.423674257292$$
$$x_{41} = -31.425150430308$$
$$x_{42} = -87.4236742574395$$
$$x_{43} = -53.4236768879087$$
$$x_{44} = -25.4320063693618$$
$$x_{45} = -95.4236742573057$$
$$x_{46} = -101.423674257294$$
$$x_{47} = -67.423674304163$$
$$x_{48} = -71.4236742721215$$
$$x_{49} = -109.423674257291$$
$$x_{50} = -15.5873652307869$$
$$x_{51} = -65.4236743406191$$
Las raíces dadas
$$x_{49} = -109.423674257291$$
$$x_{13} = -107.423674257291$$
$$x_{40} = -105.423674257292$$
$$x_{38} = -103.423674257292$$
$$x_{46} = -101.423674257294$$
$$x_{25} = -99.4236742572956$$
$$x_{8} = -97.4236742572992$$
$$x_{45} = -95.4236742573057$$
$$x_{39} = -93.4236742573173$$
$$x_{32} = -91.4236742573379$$
$$x_{14} = -89.4236742573745$$
$$x_{42} = -87.4236742574395$$
$$x_{18} = -85.4236742575551$$
$$x_{35} = -83.4236742577606$$
$$x_{19} = -81.423674258126$$
$$x_{5} = -79.4236742587756$$
$$x_{31} = -77.4236742599304$$
$$x_{1} = -75.4236742619834$$
$$x_{20} = -73.4236742656331$$
$$x_{48} = -71.4236742721215$$
$$x_{2} = -69.4236742836564$$
$$x_{47} = -67.423674304163$$
$$x_{51} = -65.4236743406191$$
$$x_{27} = -63.4236744054299$$
$$x_{37} = -61.4236745206493$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{26} = -55.4236757370122$$
$$x_{43} = -53.4236768879087$$
$$x_{11} = -51.4236789339511$$
$$x_{7} = -49.4236825713738$$
$$x_{21} = -47.4236890379465$$
$$x_{29} = -45.4237005342138$$
$$x_{10} = -43.4237209724582$$
$$x_{28} = -41.4237573084927$$
$$x_{22} = -39.423821910242$$
$$x_{36} = -37.4239367715623$$
$$x_{16} = -35.4241410129855$$
$$x_{30} = -33.4245042464747$$
$$x_{41} = -31.425150430308$$
$$x_{9} = -29.4263005801687$$
$$x_{12} = -27.4283496621804$$
$$x_{44} = -25.4320063693618$$
$$x_{17} = -23.4385515501772$$
$$x_{3} = -21.4503302630093$$
$$x_{6} = -19.4717369349091$$
$$x_{15} = -17.5113613217216$$
$$x_{50} = -15.5873652307869$$
$$x_{34} = -13.7446078221231$$
$$x_{33} = 0$$
$$x_{4} = 1$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{49}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{49} - \frac{1}{10}$$
=
$$-109.423674257291 + - \frac{1}{10}$$
=
$$-109.523674257291$$
lo sustituimos en la expresión
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
$$\frac{3}{16^{109.523674257291}} + \left(- \frac{7}{12^{109.523674257291}} + \frac{4}{9^{109.523674257291}}\right) > 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -109.423674257291$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -109.423674257291$$
$$x > -107.423674257291 \wedge x < -105.423674257292$$
$$x > -103.423674257292 \wedge x < -101.423674257294$$
$$x > -99.4236742572956 \wedge x < -97.4236742572992$$
$$x > -95.4236742573057 \wedge x < -93.4236742573173$$
$$x > -91.4236742573379 \wedge x < -89.4236742573745$$
$$x > -87.4236742574395 \wedge x < -85.4236742575551$$
$$x > -83.4236742577606 \wedge x < -81.423674258126$$
$$x > -79.4236742587756 \wedge x < -77.4236742599304$$
$$x > -75.4236742619834 \wedge x < -73.4236742656331$$
$$x > -71.4236742721215 \wedge x < -69.4236742836564$$
$$x > -67.423674304163 \wedge x < -65.4236743406191$$
$$x > -63.4236744054299 \wedge x < -61.4236745206493$$
$$x > -59.4236747254836 \wedge x < -57.4236750896338$$
$$x > -55.4236757370122 \wedge x < -53.4236768879087$$
$$x > -51.4236789339511 \wedge x < -49.4236825713738$$
$$x > -47.4236890379465 \wedge x < -45.4237005342138$$
$$x > -43.4237209724582 \wedge x < -41.4237573084927$$
$$x > -39.423821910242 \wedge x < -37.4239367715623$$
$$x > -35.4241410129855 \wedge x < -33.4245042464747$$
$$x > -31.425150430308 \wedge x < -29.4263005801687$$
$$x > -27.4283496621804 \wedge x < -25.4320063693618$$
$$x > -23.4385515501772 \wedge x < -21.4503302630093$$
$$x > -19.4717369349091 \wedge x < -17.5113613217216$$
$$x > -15.5873652307869 \wedge x < -13.7446078221231$$
$$x > 0 \wedge x < 1$$
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) = 0$$
Resolvemos:
$$x_{1} = -75.4236742619834$$
$$x_{2} = -69.4236742836564$$
$$x_{3} = -21.4503302630093$$
$$x_{4} = 1$$
$$x_{5} = -79.4236742587756$$
$$x_{6} = -19.4717369349091$$
$$x_{7} = -49.4236825713738$$
$$x_{8} = -97.4236742572992$$
$$x_{9} = -29.4263005801687$$
$$x_{10} = -43.4237209724582$$
$$x_{11} = -51.4236789339511$$
$$x_{12} = -27.4283496621804$$
$$x_{13} = -107.423674257291$$
$$x_{14} = -89.4236742573745$$
$$x_{15} = -17.5113613217216$$
$$x_{16} = -35.4241410129855$$
$$x_{17} = -23.4385515501772$$
$$x_{18} = -85.4236742575551$$
$$x_{19} = -81.423674258126$$
$$x_{20} = -73.4236742656331$$
$$x_{21} = -47.4236890379465$$
$$x_{22} = -39.423821910242$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{25} = -99.4236742572956$$
$$x_{26} = -55.4236757370122$$
$$x_{27} = -63.4236744054299$$
$$x_{28} = -41.4237573084927$$
$$x_{29} = -45.4237005342138$$
$$x_{30} = -33.4245042464747$$
$$x_{31} = -77.4236742599304$$
$$x_{32} = -91.4236742573379$$
$$x_{33} = 0$$
$$x_{34} = -13.7446078221231$$
$$x_{35} = -83.4236742577606$$
$$x_{36} = -37.4239367715623$$
$$x_{37} = -61.4236745206493$$
$$x_{38} = -103.423674257292$$
$$x_{39} = -93.4236742573173$$
$$x_{40} = -105.423674257292$$
$$x_{41} = -31.425150430308$$
$$x_{42} = -87.4236742574395$$
$$x_{43} = -53.4236768879087$$
$$x_{44} = -25.4320063693618$$
$$x_{45} = -95.4236742573057$$
$$x_{46} = -101.423674257294$$
$$x_{47} = -67.423674304163$$
$$x_{48} = -71.4236742721215$$
$$x_{49} = -109.423674257291$$
$$x_{50} = -15.5873652307869$$
$$x_{51} = -65.4236743406191$$
$$x_{1} = -75.4236742619834$$
$$x_{2} = -69.4236742836564$$
$$x_{3} = -21.4503302630093$$
$$x_{4} = 1$$
$$x_{5} = -79.4236742587756$$
$$x_{6} = -19.4717369349091$$
$$x_{7} = -49.4236825713738$$
$$x_{8} = -97.4236742572992$$
$$x_{9} = -29.4263005801687$$
$$x_{10} = -43.4237209724582$$
$$x_{11} = -51.4236789339511$$
$$x_{12} = -27.4283496621804$$
$$x_{13} = -107.423674257291$$
$$x_{14} = -89.4236742573745$$
$$x_{15} = -17.5113613217216$$
$$x_{16} = -35.4241410129855$$
$$x_{17} = -23.4385515501772$$
$$x_{18} = -85.4236742575551$$
$$x_{19} = -81.423674258126$$
$$x_{20} = -73.4236742656331$$
$$x_{21} = -47.4236890379465$$
$$x_{22} = -39.423821910242$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{25} = -99.4236742572956$$
$$x_{26} = -55.4236757370122$$
$$x_{27} = -63.4236744054299$$
$$x_{28} = -41.4237573084927$$
$$x_{29} = -45.4237005342138$$
$$x_{30} = -33.4245042464747$$
$$x_{31} = -77.4236742599304$$
$$x_{32} = -91.4236742573379$$
$$x_{33} = 0$$
$$x_{34} = -13.7446078221231$$
$$x_{35} = -83.4236742577606$$
$$x_{36} = -37.4239367715623$$
$$x_{37} = -61.4236745206493$$
$$x_{38} = -103.423674257292$$
$$x_{39} = -93.4236742573173$$
$$x_{40} = -105.423674257292$$
$$x_{41} = -31.425150430308$$
$$x_{42} = -87.4236742574395$$
$$x_{43} = -53.4236768879087$$
$$x_{44} = -25.4320063693618$$
$$x_{45} = -95.4236742573057$$
$$x_{46} = -101.423674257294$$
$$x_{47} = -67.423674304163$$
$$x_{48} = -71.4236742721215$$
$$x_{49} = -109.423674257291$$
$$x_{50} = -15.5873652307869$$
$$x_{51} = -65.4236743406191$$
Las raíces dadas
$$x_{49} = -109.423674257291$$
$$x_{13} = -107.423674257291$$
$$x_{40} = -105.423674257292$$
$$x_{38} = -103.423674257292$$
$$x_{46} = -101.423674257294$$
$$x_{25} = -99.4236742572956$$
$$x_{8} = -97.4236742572992$$
$$x_{45} = -95.4236742573057$$
$$x_{39} = -93.4236742573173$$
$$x_{32} = -91.4236742573379$$
$$x_{14} = -89.4236742573745$$
$$x_{42} = -87.4236742574395$$
$$x_{18} = -85.4236742575551$$
$$x_{35} = -83.4236742577606$$
$$x_{19} = -81.423674258126$$
$$x_{5} = -79.4236742587756$$
$$x_{31} = -77.4236742599304$$
$$x_{1} = -75.4236742619834$$
$$x_{20} = -73.4236742656331$$
$$x_{48} = -71.4236742721215$$
$$x_{2} = -69.4236742836564$$
$$x_{47} = -67.423674304163$$
$$x_{51} = -65.4236743406191$$
$$x_{27} = -63.4236744054299$$
$$x_{37} = -61.4236745206493$$
$$x_{23} = -59.4236747254836$$
$$x_{24} = -57.4236750896338$$
$$x_{26} = -55.4236757370122$$
$$x_{43} = -53.4236768879087$$
$$x_{11} = -51.4236789339511$$
$$x_{7} = -49.4236825713738$$
$$x_{21} = -47.4236890379465$$
$$x_{29} = -45.4237005342138$$
$$x_{10} = -43.4237209724582$$
$$x_{28} = -41.4237573084927$$
$$x_{22} = -39.423821910242$$
$$x_{36} = -37.4239367715623$$
$$x_{16} = -35.4241410129855$$
$$x_{30} = -33.4245042464747$$
$$x_{41} = -31.425150430308$$
$$x_{9} = -29.4263005801687$$
$$x_{12} = -27.4283496621804$$
$$x_{44} = -25.4320063693618$$
$$x_{17} = -23.4385515501772$$
$$x_{3} = -21.4503302630093$$
$$x_{6} = -19.4717369349091$$
$$x_{15} = -17.5113613217216$$
$$x_{50} = -15.5873652307869$$
$$x_{34} = -13.7446078221231$$
$$x_{33} = 0$$
$$x_{4} = 1$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{49}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{49} - \frac{1}{10}$$
=
$$-109.423674257291 + - \frac{1}{10}$$
=
$$-109.523674257291$$
lo sustituimos en la expresión
$$3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
$$\frac{3}{16^{109.523674257291}} + \left(- \frac{7}{12^{109.523674257291}} + \frac{4}{9^{109.523674257291}}\right) > 0$$
1.23002581161176e-104 > 0
significa que una de las soluciones de nuestra ecuación será con:
$$x < -109.423674257291$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x49 x13 x40 x38 x46 x25 x8 x45 x39 x32 x14 x42 x18 x35 x19 x5 x31 x1 x20 x48 x2 x47 x51 x27 x37 x23 x24 x26 x43 x11 x7 x21 x29 x10 x28 x22 x36 x16 x30 x41 x9 x12 x44 x17 x3 x6 x15 x50 x34 x33 x4Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -109.423674257291$$
$$x > -107.423674257291 \wedge x < -105.423674257292$$
$$x > -103.423674257292 \wedge x < -101.423674257294$$
$$x > -99.4236742572956 \wedge x < -97.4236742572992$$
$$x > -95.4236742573057 \wedge x < -93.4236742573173$$
$$x > -91.4236742573379 \wedge x < -89.4236742573745$$
$$x > -87.4236742574395 \wedge x < -85.4236742575551$$
$$x > -83.4236742577606 \wedge x < -81.423674258126$$
$$x > -79.4236742587756 \wedge x < -77.4236742599304$$
$$x > -75.4236742619834 \wedge x < -73.4236742656331$$
$$x > -71.4236742721215 \wedge x < -69.4236742836564$$
$$x > -67.423674304163 \wedge x < -65.4236743406191$$
$$x > -63.4236744054299 \wedge x < -61.4236745206493$$
$$x > -59.4236747254836 \wedge x < -57.4236750896338$$
$$x > -55.4236757370122 \wedge x < -53.4236768879087$$
$$x > -51.4236789339511 \wedge x < -49.4236825713738$$
$$x > -47.4236890379465 \wedge x < -45.4237005342138$$
$$x > -43.4237209724582 \wedge x < -41.4237573084927$$
$$x > -39.423821910242 \wedge x < -37.4239367715623$$
$$x > -35.4241410129855 \wedge x < -33.4245042464747$$
$$x > -31.425150430308 \wedge x < -29.4263005801687$$
$$x > -27.4283496621804 \wedge x < -25.4320063693618$$
$$x > -23.4385515501772 \wedge x < -21.4503302630093$$
$$x > -19.4717369349091 \wedge x < -17.5113613217216$$
$$x > -15.5873652307869 \wedge x < -13.7446078221231$$
$$x > 0 \wedge x < 1$$
Solución de la desigualdad en el gráfico
Gráfico