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4^x-4*2^x+3+1/4^x-4*2^x+5>0
Resolver desigualdades/ 4^x-4*2^x+3+1/4^x-4*2^x+5>0

4^x-4*2^x+3+1/4^x-4*2^x+5>0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
 x      x        -x      x        
4  - 4*2  + 3 + 4   - 4*2  + 5 > 0
(−4⋅2x+(((−4⋅2x+4x)+3)+(14)x))+5>0\left(- 4 \cdot 2^{x} + \left(\left(\left(- 4 \cdot 2^{x} + 4^{x}\right) + 3\right) + \left(\frac{1}{4}\right)^{x}\right)\right) + 5 > 0 
-4*2^x - 4*2^x + 4^x + 3 + (1/4)^x + 5 > 0
Solución de la desigualdad en el gráfico
-5.0-4.0-3.0-2.0-1.05.00.01.02.03.04.0-2525
Respuesta rápida [src] 
  /   /           /                                                                                        _____________________________________________________________________________________________________________________________\    \         /                                                                                        _____________________________________________________________________________________________________________________________\\
  |   |           |                                                                                       /             ________________                                                                                                |    |         |                                                                                       /             ________________                                                                                                ||
  |   |           |                                                                                      /             /         ______                                                                                                 |    |         |                                                                                      /             /         ______                                                                                                 ||
  |   |           |                                                                                     /   64        /  136   \/ 1293                                     64                                              38           |    |         |                                                                                     /   64        /  136   \/ 1293                                     64                                              38           ||
  |   |           |                                                                                    /    -- - 2*3 /   --- + --------  + ------------------------------------------------------------------ - ----------------------- |    |         |                                                                                    /    -- - 2*3 /   --- + --------  + ------------------------------------------------------------------ - ----------------------- ||
  |   |           |              ________________________________________________________             /     3      \/     27      9                  ________________________________________________________          ________________ |    |         |              ________________________________________________________             /     3      \/     27      9                  ________________________________________________________          ________________ ||
  |   |           |             /             ________________                                       /                                              /             ________________                                    /         ______  |    |         |             /             ________________                                       /                                              /             ________________                                    /         ______  ||
  |   |           |            /             /         ______                                       /                                              /             /         ______                                    /  136   \/ 1293   |    |         |            /             /         ______                                       /                                              /             /         ______                                    /  136   \/ 1293   ||
  |   |           |           /   32        /  136   \/ 1293                38                     /                                              /   32        /  136   \/ 1293                38              9*3 /   --- + --------  |    |         |           /   32        /  136   \/ 1293                38                     /                                              /   32        /  136   \/ 1293                38              9*3 /   --- + --------  ||
  |   |           |          /    -- + 2*3 /   --- + --------  + -----------------------          /                                              /    -- + 2*3 /   --- + --------  + -----------------------      \/     27      9      |    |         |          /    -- + 2*3 /   --- + --------  + -----------------------          /                                              /    -- + 2*3 /   --- + --------  + -----------------------      \/     27      9      ||
  |   |           |         /     3      \/     27      9               ________________         /                                              /     3      \/     27      9               ________________                            |    |         |         /     3      \/     27      9               ________________         /                                              /     3      \/     27      9               ________________                            ||
  |   |           |        /                                           /         ______         /                                              /                                           /         ______                             |    |         |        /                                           /         ______         /                                              /                                           /         ______                             ||
  |   |           |       /                                           /  136   \/ 1293         /                                              /                                           /  136   \/ 1293                              |    |         |       /                                           /  136   \/ 1293         /                                              /                                           /  136   \/ 1293                              ||
  |   |           |      /                                       9*3 /   --- + --------       /                                              /                                       9*3 /   --- + --------                             |    |         |      /                                       9*3 /   --- + --------       /                                              /                                       9*3 /   --- + --------                             ||
  |   |           |    \/                                          \/     27      9         \/                                             \/                                          \/     27      9                                 |    |         |    \/                                          \/     27      9         \/                                             \/                                          \/     27      9                                 ||
  |   |        log|2 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------|    |      log|2 + ------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------||
  |   |           \                                    2                                                                                                         2                                                                      /    |         \                                    2                                                                                                         2                                                                      /|
Or|And|x < oo, -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- < x|, x < --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  \   \                                                                                                                  log(2)                                                                                                              /                                                                                                                log(2)                                                                                                          /
(x<∞∧log⁡(2+38912939+136273+212939+136273+3232+−212939+136273−38912939+136273+6438912939+136273+212939+136273+323+6432)log⁡(2)<x)∨x<log⁡(−−212939+136273−38912939+136273+6438912939+136273+212939+136273+323+6432+2+38912939+136273+212939+136273+3232)log⁡(2)\left(x < \infty \wedge \frac{\log{\left(2 + \frac{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} - \frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + \frac{64}{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}} + \frac{64}{3}}}{2} \right)}}{\log{\left(2 \right)}} < x\right) \vee x < \frac{\log{\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} - \frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + \frac{64}{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}} + \frac{64}{3}}}{2} + 2 + \frac{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}}{2} \right)}}{\log{\left(2 \right)}} 
(x < log(2 + sqrt(32/3 + 2*(136/27 + sqrt(1293)/9)^(1/3) + 38/(9*(136/27 + sqrt(1293)/9)^(1/3)))/2 - sqrt(64/3 - 2*(136/27 + sqrt(1293)/9)^(1/3) + 64/sqrt(32/3 + 2*(136/27 + sqrt(1293)/9)^(1/3) + 38/(9*(136/27 + sqrt(1293)/9)^(1/3))) - 38/(9*(136/27 + sqrt(1293)/9)^(1/3)))/2)/log(2))∨((x < oo)∧(log(2 + sqrt(32/3 + 2*(136/27 + sqrt(1293)/9)^(1/3) + 38/(9*(136/27 + sqrt(1293)/9)^(1/3)))/2 + sqrt(64/3 - 2*(136/27 + sqrt(1293)/9)^(1/3) + 64/sqrt(32/3 + 2*(136/27 + sqrt(1293)/9)^(1/3) + 38/(9*(136/27 + sqrt(1293)/9)^(1/3))) - 38/(9*(136/27 + sqrt(1293)/9)^(1/3)))/2)/log(2) < x))
Respuesta rápida 2 [src] 
         /                                                                                        _____________________________________________________________________________________________________________________________\        /                                                                                        _____________________________________________________________________________________________________________________________\     
         |                                                                                       /             ________________                                                                                                |        |                                                                                       /             ________________                                                                                                |     
         |                                                                                      /             /         ______                                                                                                 |        |                                                                                      /             /         ______                                                                                                 |     
         |                                                                                     /   64        /  136   \/ 1293                                     64                                              38           |        |                                                                                     /   64        /  136   \/ 1293                                     64                                              38           |     
         |                                                                                    /    -- - 2*3 /   --- + --------  + ------------------------------------------------------------------ - ----------------------- |        |                                                                                    /    -- - 2*3 /   --- + --------  + ------------------------------------------------------------------ - ----------------------- |     
         |              ________________________________________________________             /     3      \/     27      9                  ________________________________________________________          ________________ |        |              ________________________________________________________             /     3      \/     27      9                  ________________________________________________________          ________________ |     
         |             /             ________________                                       /                                              /             ________________                                    /         ______  |        |             /             ________________                                       /                                              /             ________________                                    /         ______  |     
         |            /             /         ______                                       /                                              /             /         ______                                    /  136   \/ 1293   |        |            /             /         ______                                       /                                              /             /         ______                                    /  136   \/ 1293   |     
         |           /   32        /  136   \/ 1293                38                     /                                              /   32        /  136   \/ 1293                38              9*3 /   --- + --------  |        |           /   32        /  136   \/ 1293                38                     /                                              /   32        /  136   \/ 1293                38              9*3 /   --- + --------  |     
         |          /    -- + 2*3 /   --- + --------  + -----------------------          /                                              /    -- + 2*3 /   --- + --------  + -----------------------      \/     27      9      |        |          /    -- + 2*3 /   --- + --------  + -----------------------          /                                              /    -- + 2*3 /   --- + --------  + -----------------------      \/     27      9      |     
         |         /     3      \/     27      9               ________________         /                                              /     3      \/     27      9               ________________                            |        |         /     3      \/     27      9               ________________         /                                              /     3      \/     27      9               ________________                            |     
         |        /                                           /         ______         /                                              /                                           /         ______                             |        |        /                                           /         ______         /                                              /                                           /         ______                             |     
         |       /                                           /  136   \/ 1293         /                                              /                                           /  136   \/ 1293                              |        |       /                                           /  136   \/ 1293         /                                              /                                           /  136   \/ 1293                              |     
         |      /                                       9*3 /   --- + --------       /                                              /                                       9*3 /   --- + --------                             |        |      /                                       9*3 /   --- + --------       /                                              /                                       9*3 /   --- + --------                             |     
         |    \/                                          \/     27      9         \/                                             \/                                          \/     27      9                                 |        |    \/                                          \/     27      9         \/                                             \/                                          \/     27      9                                 |     
      log|2 + ------------------------------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------------|     log|2 + ------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------|     
         \                                    2                                                                                                         2                                                                      /        \                                    2                                                                                                         2                                                                      /     
(-oo, --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------) U (--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, oo)
                                                                                                                log(2)                                                                                                                                                                                                                         log(2)
x in (−∞,log⁡(−−212939+136273−38912939+136273+6438912939+136273+212939+136273+323+6432+2+38912939+136273+212939+136273+3232)log⁡(2))∪(log⁡(2+38912939+136273+212939+136273+3232+−212939+136273−38912939+136273+6438912939+136273+212939+136273+323+6432)log⁡(2),∞)x\ in\ \left(-\infty, \frac{\log{\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} - \frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + \frac{64}{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}} + \frac{64}{3}}}{2} + 2 + \frac{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}}{2} \right)}}{\log{\left(2 \right)}}\right) \cup \left(\frac{\log{\left(2 + \frac{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} - \frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + \frac{64}{\sqrt{\frac{38}{9 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}}} + 2 \sqrt[3]{\frac{\sqrt{1293}}{9} + \frac{136}{27}} + \frac{32}{3}}} + \frac{64}{3}}}{2} \right)}}{\log{\left(2 \right)}}, \infty\right) 
x in Union(Interval.open(-oo, log(-sqrt(-2*(sqrt(1293)/9 + 136/27)^(1/3) - 38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 64/sqrt(38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 2*(sqrt(1293)/9 + 136/27)^(1/3) + 32/3) + 64/3)/2 + 2 + sqrt(38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 2*(sqrt(1293)/9 + 136/27)^(1/3) + 32/3)/2)/log(2)), Interval.open(log(2 + sqrt(38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 2*(sqrt(1293)/9 + 136/27)^(1/3) + 32/3)/2 + sqrt(-2*(sqrt(1293)/9 + 136/27)^(1/3) - 38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 64/sqrt(38/(9*(sqrt(1293)/9 + 136/27)^(1/3)) + 2*(sqrt(1293)/9 + 136/27)^(1/3) + 32/3) + 64/3)/2)/log(2), oo))
Gráfico
4^x-4*2^x+3+1/4^x-4*2^x+5>0 desigualdades
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