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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 menos 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 menos 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:
$$x_{1} = -65.4236743406191$$
$$x_{2} = -47.4236890382136$$
$$x_{3} = -105.423674257292$$
$$x_{4} = -57.4236750896346$$
$$x_{5} = -109.423674257291$$
$$x_{6} = -75.4236742619834$$
$$x_{7} = -59.4236747254839$$
$$x_{8} = -103.423674257292$$
$$x_{9} = -13.9820313419982$$
$$x_{10} = -19.474722822855$$
$$x_{11} = -29.4263090371779$$
$$x_{12} = -35.4241412794753$$
$$x_{13} = -81.423674258126$$
$$x_{14} = -99.4236742572956$$
$$x_{15} = -85.4236742575551$$
$$x_{16} = -33.4245050894545$$
$$x_{17} = -45.423700535058$$
$$x_{18} = -79.4236742587756$$
$$x_{19} = -71.4236742721215$$
$$x_{20} = -101.423674257294$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{23} = -77.4236742599304$$
$$x_{24} = -2.58911276684519$$
$$x_{25} = -53.4236768879171$$
$$x_{26} = -91.4236742573379$$
$$x_{27} = -17.5218308295858$$
$$x_{28} = -69.4236742836564$$
$$x_{29} = -49.4236825714583$$
$$x_{30} = -27.4283765237765$$
$$x_{31} = -15.6284855252173$$
$$x_{32} = -39.4238219369005$$
$$x_{33} = -83.4236742577606$$
$$x_{34} = -61.4236745206493$$
$$x_{35} = -25.4320920244927$$
$$x_{36} = -67.423674304163$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{39} = -63.42367440543$$
$$x_{40} = -73.4236742656331$$
$$x_{41} = -43.4237209751264$$
$$x_{42} = -107.423674257291$$
$$x_{43} = -21.451225371224$$
$$x_{44} = -55.4236757370149$$
$$x_{45} = -37.4239368558396$$
$$x_{46} = -51.4236789339779$$
$$x_{47} = -23.4388266357446$$
$$x_{48} = -31.4251530987113$$
$$x_{49} = -41.4237573169263$$
$$x_{50} = -93.4236742573173$$
$$x_{1} = -65.4236743406191$$
$$x_{2} = -47.4236890382136$$
$$x_{3} = -105.423674257292$$
$$x_{4} = -57.4236750896346$$
$$x_{5} = -109.423674257291$$
$$x_{6} = -75.4236742619834$$
$$x_{7} = -59.4236747254839$$
$$x_{8} = -103.423674257292$$
$$x_{9} = -13.9820313419982$$
$$x_{10} = -19.474722822855$$
$$x_{11} = -29.4263090371779$$
$$x_{12} = -35.4241412794753$$
$$x_{13} = -81.423674258126$$
$$x_{14} = -99.4236742572956$$
$$x_{15} = -85.4236742575551$$
$$x_{16} = -33.4245050894545$$
$$x_{17} = -45.423700535058$$
$$x_{18} = -79.4236742587756$$
$$x_{19} = -71.4236742721215$$
$$x_{20} = -101.423674257294$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{23} = -77.4236742599304$$
$$x_{24} = -2.58911276684519$$
$$x_{25} = -53.4236768879171$$
$$x_{26} = -91.4236742573379$$
$$x_{27} = -17.5218308295858$$
$$x_{28} = -69.4236742836564$$
$$x_{29} = -49.4236825714583$$
$$x_{30} = -27.4283765237765$$
$$x_{31} = -15.6284855252173$$
$$x_{32} = -39.4238219369005$$
$$x_{33} = -83.4236742577606$$
$$x_{34} = -61.4236745206493$$
$$x_{35} = -25.4320920244927$$
$$x_{36} = -67.423674304163$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{39} = -63.42367440543$$
$$x_{40} = -73.4236742656331$$
$$x_{41} = -43.4237209751264$$
$$x_{42} = -107.423674257291$$
$$x_{43} = -21.451225371224$$
$$x_{44} = -55.4236757370149$$
$$x_{45} = -37.4239368558396$$
$$x_{46} = -51.4236789339779$$
$$x_{47} = -23.4388266357446$$
$$x_{48} = -31.4251530987113$$
$$x_{49} = -41.4237573169263$$
$$x_{50} = -93.4236742573173$$
Las raíces dadas
$$x_{5} = -109.423674257291$$
$$x_{42} = -107.423674257291$$
$$x_{3} = -105.423674257292$$
$$x_{8} = -103.423674257292$$
$$x_{20} = -101.423674257294$$
$$x_{14} = -99.4236742572956$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{50} = -93.4236742573173$$
$$x_{26} = -91.4236742573379$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{15} = -85.4236742575551$$
$$x_{33} = -83.4236742577606$$
$$x_{13} = -81.423674258126$$
$$x_{18} = -79.4236742587756$$
$$x_{23} = -77.4236742599304$$
$$x_{6} = -75.4236742619834$$
$$x_{40} = -73.4236742656331$$
$$x_{19} = -71.4236742721215$$
$$x_{28} = -69.4236742836564$$
$$x_{36} = -67.423674304163$$
$$x_{1} = -65.4236743406191$$
$$x_{39} = -63.42367440543$$
$$x_{34} = -61.4236745206493$$
$$x_{7} = -59.4236747254839$$
$$x_{4} = -57.4236750896346$$
$$x_{44} = -55.4236757370149$$
$$x_{25} = -53.4236768879171$$
$$x_{46} = -51.4236789339779$$
$$x_{29} = -49.4236825714583$$
$$x_{2} = -47.4236890382136$$
$$x_{17} = -45.423700535058$$
$$x_{41} = -43.4237209751264$$
$$x_{49} = -41.4237573169263$$
$$x_{32} = -39.4238219369005$$
$$x_{45} = -37.4239368558396$$
$$x_{12} = -35.4241412794753$$
$$x_{16} = -33.4245050894545$$
$$x_{48} = -31.4251530987113$$
$$x_{11} = -29.4263090371779$$
$$x_{30} = -27.4283765237765$$
$$x_{35} = -25.4320920244927$$
$$x_{47} = -23.4388266357446$$
$$x_{43} = -21.451225371224$$
$$x_{10} = -19.474722822855$$
$$x_{27} = -17.5218308295858$$
$$x_{31} = -15.6284855252173$$
$$x_{9} = -13.9820313419982$$
$$x_{24} = -2.58911276684519$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{5}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{5} - \frac{1}{10}$$
=
$$-109.423674257291 + - \frac{1}{10}$$
=
$$-109.523674257291$$
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:
$$x < -109.423674257291$$
$$x > -107.423674257291 \wedge x < -105.423674257292$$
$$x > -103.423674257292 \wedge x < -101.423674257294$$
$$x > -99.4236742572956 \wedge x < -97.4236742572992$$
$$x > -95.4236742573057 \wedge x < -93.4236742573173$$
$$x > -91.4236742573379 \wedge x < -89.4236742573745$$
$$x > -87.4236742574395 \wedge x < -85.4236742575551$$
$$x > -83.4236742577606 \wedge x < -81.423674258126$$
$$x > -79.4236742587756 \wedge x < -77.4236742599304$$
$$x > -75.4236742619834 \wedge x < -73.4236742656331$$
$$x > -71.4236742721215 \wedge x < -69.4236742836564$$
$$x > -67.423674304163 \wedge x < -65.4236743406191$$
$$x > -63.42367440543 \wedge x < -61.4236745206493$$
$$x > -59.4236747254839 \wedge x < -57.4236750896346$$
$$x > -55.4236757370149 \wedge x < -53.4236768879171$$
$$x > -51.4236789339779 \wedge x < -49.4236825714583$$
$$x > -47.4236890382136 \wedge x < -45.423700535058$$
$$x > -43.4237209751264 \wedge x < -41.4237573169263$$
$$x > -39.4238219369005 \wedge x < -37.4239368558396$$
$$x > -35.4241412794753 \wedge x < -33.4245050894545$$
$$x > -31.4251530987113 \wedge x < -29.4263090371779$$
$$x > -27.4283765237765 \wedge x < -25.4320920244927$$
$$x > -23.4388266357446 \wedge x < -21.451225371224$$
$$x > -19.474722822855 \wedge x < -17.5218308295858$$
$$x > -15.6284855252173 \wedge x < -13.9820313419982$$
$$x > -2.58911276684519$$
$$- 3 \cdot 16^{x} + \left(- 7 \cdot 12^{x} + 4 \cdot 9^{x}\right) > 0$$
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:
$$x_{1} = -65.4236743406191$$
$$x_{2} = -47.4236890382136$$
$$x_{3} = -105.423674257292$$
$$x_{4} = -57.4236750896346$$
$$x_{5} = -109.423674257291$$
$$x_{6} = -75.4236742619834$$
$$x_{7} = -59.4236747254839$$
$$x_{8} = -103.423674257292$$
$$x_{9} = -13.9820313419982$$
$$x_{10} = -19.474722822855$$
$$x_{11} = -29.4263090371779$$
$$x_{12} = -35.4241412794753$$
$$x_{13} = -81.423674258126$$
$$x_{14} = -99.4236742572956$$
$$x_{15} = -85.4236742575551$$
$$x_{16} = -33.4245050894545$$
$$x_{17} = -45.423700535058$$
$$x_{18} = -79.4236742587756$$
$$x_{19} = -71.4236742721215$$
$$x_{20} = -101.423674257294$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{23} = -77.4236742599304$$
$$x_{24} = -2.58911276684519$$
$$x_{25} = -53.4236768879171$$
$$x_{26} = -91.4236742573379$$
$$x_{27} = -17.5218308295858$$
$$x_{28} = -69.4236742836564$$
$$x_{29} = -49.4236825714583$$
$$x_{30} = -27.4283765237765$$
$$x_{31} = -15.6284855252173$$
$$x_{32} = -39.4238219369005$$
$$x_{33} = -83.4236742577606$$
$$x_{34} = -61.4236745206493$$
$$x_{35} = -25.4320920244927$$
$$x_{36} = -67.423674304163$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{39} = -63.42367440543$$
$$x_{40} = -73.4236742656331$$
$$x_{41} = -43.4237209751264$$
$$x_{42} = -107.423674257291$$
$$x_{43} = -21.451225371224$$
$$x_{44} = -55.4236757370149$$
$$x_{45} = -37.4239368558396$$
$$x_{46} = -51.4236789339779$$
$$x_{47} = -23.4388266357446$$
$$x_{48} = -31.4251530987113$$
$$x_{49} = -41.4237573169263$$
$$x_{50} = -93.4236742573173$$
$$x_{1} = -65.4236743406191$$
$$x_{2} = -47.4236890382136$$
$$x_{3} = -105.423674257292$$
$$x_{4} = -57.4236750896346$$
$$x_{5} = -109.423674257291$$
$$x_{6} = -75.4236742619834$$
$$x_{7} = -59.4236747254839$$
$$x_{8} = -103.423674257292$$
$$x_{9} = -13.9820313419982$$
$$x_{10} = -19.474722822855$$
$$x_{11} = -29.4263090371779$$
$$x_{12} = -35.4241412794753$$
$$x_{13} = -81.423674258126$$
$$x_{14} = -99.4236742572956$$
$$x_{15} = -85.4236742575551$$
$$x_{16} = -33.4245050894545$$
$$x_{17} = -45.423700535058$$
$$x_{18} = -79.4236742587756$$
$$x_{19} = -71.4236742721215$$
$$x_{20} = -101.423674257294$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{23} = -77.4236742599304$$
$$x_{24} = -2.58911276684519$$
$$x_{25} = -53.4236768879171$$
$$x_{26} = -91.4236742573379$$
$$x_{27} = -17.5218308295858$$
$$x_{28} = -69.4236742836564$$
$$x_{29} = -49.4236825714583$$
$$x_{30} = -27.4283765237765$$
$$x_{31} = -15.6284855252173$$
$$x_{32} = -39.4238219369005$$
$$x_{33} = -83.4236742577606$$
$$x_{34} = -61.4236745206493$$
$$x_{35} = -25.4320920244927$$
$$x_{36} = -67.423674304163$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{39} = -63.42367440543$$
$$x_{40} = -73.4236742656331$$
$$x_{41} = -43.4237209751264$$
$$x_{42} = -107.423674257291$$
$$x_{43} = -21.451225371224$$
$$x_{44} = -55.4236757370149$$
$$x_{45} = -37.4239368558396$$
$$x_{46} = -51.4236789339779$$
$$x_{47} = -23.4388266357446$$
$$x_{48} = -31.4251530987113$$
$$x_{49} = -41.4237573169263$$
$$x_{50} = -93.4236742573173$$
Las raíces dadas
$$x_{5} = -109.423674257291$$
$$x_{42} = -107.423674257291$$
$$x_{3} = -105.423674257292$$
$$x_{8} = -103.423674257292$$
$$x_{20} = -101.423674257294$$
$$x_{14} = -99.4236742572956$$
$$x_{21} = -97.4236742572992$$
$$x_{22} = -95.4236742573057$$
$$x_{50} = -93.4236742573173$$
$$x_{26} = -91.4236742573379$$
$$x_{37} = -89.4236742573745$$
$$x_{38} = -87.4236742574395$$
$$x_{15} = -85.4236742575551$$
$$x_{33} = -83.4236742577606$$
$$x_{13} = -81.423674258126$$
$$x_{18} = -79.4236742587756$$
$$x_{23} = -77.4236742599304$$
$$x_{6} = -75.4236742619834$$
$$x_{40} = -73.4236742656331$$
$$x_{19} = -71.4236742721215$$
$$x_{28} = -69.4236742836564$$
$$x_{36} = -67.423674304163$$
$$x_{1} = -65.4236743406191$$
$$x_{39} = -63.42367440543$$
$$x_{34} = -61.4236745206493$$
$$x_{7} = -59.4236747254839$$
$$x_{4} = -57.4236750896346$$
$$x_{44} = -55.4236757370149$$
$$x_{25} = -53.4236768879171$$
$$x_{46} = -51.4236789339779$$
$$x_{29} = -49.4236825714583$$
$$x_{2} = -47.4236890382136$$
$$x_{17} = -45.423700535058$$
$$x_{41} = -43.4237209751264$$
$$x_{49} = -41.4237573169263$$
$$x_{32} = -39.4238219369005$$
$$x_{45} = -37.4239368558396$$
$$x_{12} = -35.4241412794753$$
$$x_{16} = -33.4245050894545$$
$$x_{48} = -31.4251530987113$$
$$x_{11} = -29.4263090371779$$
$$x_{30} = -27.4283765237765$$
$$x_{35} = -25.4320920244927$$
$$x_{47} = -23.4388266357446$$
$$x_{43} = -21.451225371224$$
$$x_{10} = -19.474722822855$$
$$x_{27} = -17.5218308295858$$
$$x_{31} = -15.6284855252173$$
$$x_{9} = -13.9820313419982$$
$$x_{24} = -2.58911276684519$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{5}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{5} - \frac{1}{10}$$
=
$$-109.423674257291 + - \frac{1}{10}$$
=
$$-109.523674257291$$
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-------
x5 x42 x3 x8 x20 x14 x21 x22 x50 x26 x37 x38 x15 x33 x13 x18 x23 x6 x40 x19 x28 x36 x1 x39 x34 x7 x4 x44 x25 x46 x29 x2 x17 x41 x49 x32 x45 x12 x16 x48 x11 x30 x35 x47 x43 x10 x27 x31 x9 x24Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -109.423674257291$$
$$x > -107.423674257291 \wedge x < -105.423674257292$$
$$x > -103.423674257292 \wedge x < -101.423674257294$$
$$x > -99.4236742572956 \wedge x < -97.4236742572992$$
$$x > -95.4236742573057 \wedge x < -93.4236742573173$$
$$x > -91.4236742573379 \wedge x < -89.4236742573745$$
$$x > -87.4236742574395 \wedge x < -85.4236742575551$$
$$x > -83.4236742577606 \wedge x < -81.423674258126$$
$$x > -79.4236742587756 \wedge x < -77.4236742599304$$
$$x > -75.4236742619834 \wedge x < -73.4236742656331$$
$$x > -71.4236742721215 \wedge x < -69.4236742836564$$
$$x > -67.423674304163 \wedge x < -65.4236743406191$$
$$x > -63.42367440543 \wedge x < -61.4236745206493$$
$$x > -59.4236747254839 \wedge x < -57.4236750896346$$
$$x > -55.4236757370149 \wedge x < -53.4236768879171$$
$$x > -51.4236789339779 \wedge x < -49.4236825714583$$
$$x > -47.4236890382136 \wedge x < -45.423700535058$$
$$x > -43.4237209751264 \wedge x < -41.4237573169263$$
$$x > -39.4238219369005 \wedge x < -37.4239368558396$$
$$x > -35.4241412794753 \wedge x < -33.4245050894545$$
$$x > -31.4251530987113 \wedge x < -29.4263090371779$$
$$x > -27.4283765237765 \wedge x < -25.4320920244927$$
$$x > -23.4388266357446 \wedge x < -21.451225371224$$
$$x > -19.474722822855 \wedge x < -17.5218308295858$$
$$x > -15.6284855252173 \wedge x < -13.9820313419982$$
$$x > -2.58911276684519$$
Solución de la desigualdad en el gráfico