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Resolver desigualdades/ log(x^2+x,x^2-2x+1)<=2

log(x^2+x,x^2-2x+1)<=2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
      / 2    \        
   log\x  + x/        
----------------- <= 2
   / 2          \     
log\x  - 2*x + 1/
log⁡(x2+x)log⁡((x2−2x)+1)≤2\frac{\log{\left(x^{2} + x \right)}}{\log{\left(\left(x^{2} - 2 x\right) + 1 \right)}} \leq 2 
log(x^2 + x)/log(x^2 - 2*x + 1) <= 2
Solución de la desigualdad en el gráfico
0-30-20-1010203040-20002000
Respuesta rápida 2 [src] 
                                  __________________________________________________________________________________________________________________                                                                                                                                                                     __________________________________________________________________________________________________________________     
                                 /             ________________                                  ___                                     3 ___                                                                                                                                                                          /             ________________                                  ___                                     3 ___           
                   ___          /       2/3 3 /          _____                              36*\/ 6                                   46*\/ 2                                                                                                                                                             ___          /       2/3 3 /          _____                              36*\/ 6                                   46*\/ 2            
                 \/ 6 *        /   8 - 2   *\/  97 + 9*\/ 717   + ----------------------------------------------------------- + -------------------                                                                                                                                                     \/ 6 *        /   8 - 2   *\/  97 + 9*\/ 717   + ----------------------------------------------------------- + -------------------      
                              /                                          ____________________________________________________      ________________                 ____________________________________________________                         ____________________________________________________                /                                          ____________________________________________________      ________________      
                             /                                          /             ________________            3 ___         3 /          _____                 /             ________________            3 ___                              /             ________________            3 ___                     /                                          /             ________________            3 ___         3 /          _____       
                            /                                          /       2/3 3 /          _____          46*\/ 2          \/  97 + 9*\/ 717        ___      /       2/3 3 /          _____          46*\/ 2                     ___      /       2/3 3 /          _____          46*\/ 2                     /                                          /       2/3 3 /          _____          46*\/ 2          \/  97 + 9*\/ 717        
                           /                                          /   4 + 2   *\/  97 + 9*\/ 717   - -------------------                           \/ 6 *    /   4 + 2   *\/  97 + 9*\/ 717   - -------------------             \/ 6 *    /   4 + 2   *\/  97 + 9*\/ 717   - -------------------              /                                          /   4 + 2   *\/  97 + 9*\/ 717   - -------------------                             
                          /                                          /                                      ________________                                    /                                      ________________                      /                                      ________________             /                                          /                                      ________________                             
                         /                                          /                                    3 /          _____                                    /                                    3 /          _____                      /                                    3 /          _____             /                                          /                                    3 /          _____                              
                       \/                                         \/                                     \/  97 + 9*\/ 717                                   \/                                     \/  97 + 9*\/ 717                     \/                                     \/  97 + 9*\/ 717            \/                                         \/                                     \/  97 + 9*\/ 717                               
(-oo, -1) U [1 - ----------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------, 2) U [1 + ----------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------, oo)
                                                                                  12                                                                                                   12                                                                           12                                                                                                   12
x in (−∞,−1)∪[−6−22397+97173+8+462397+97173+366−462397+97173+4+22397+9717312+6−462397+97173+4+22397+9717312+1,2)∪[6−462397+97173+4+22397+9717312+1+6−22397+97173+8+462397+97173+366−462397+97173+4+22397+9717312,∞)x\ in\ \left(-\infty, -1\right) \cup \left[- \frac{\sqrt{6} \sqrt{- 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}} + 8 + \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + \frac{36 \sqrt{6}}{\sqrt{- \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + 4 + 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}}}}}}{12} + \frac{\sqrt{6} \sqrt{- \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + 4 + 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}}}}{12} + 1, 2\right) \cup \left[\frac{\sqrt{6} \sqrt{- \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + 4 + 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}}}}{12} + 1 + \frac{\sqrt{6} \sqrt{- 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}} + 8 + \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + \frac{36 \sqrt{6}}{\sqrt{- \frac{46 \sqrt[3]{2}}{\sqrt[3]{97 + 9 \sqrt{717}}} + 4 + 2^{\frac{2}{3}} \sqrt[3]{97 + 9 \sqrt{717}}}}}}{12}, \infty\right) 
x in Union(Interval.open(-oo, -1), Interval(sqrt(6)*sqrt(-46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 4 + 2^(2/3)*(97 + 9*sqrt(717))^(1/3))/12 + 1 + sqrt(6)*sqrt(-2^(2/3)*(97 + 9*sqrt(717))^(1/3) + 8 + 46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 36*sqrt(6)/sqrt(-46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 4 + 2^(2/3)*(97 + 9*sqrt(717))^(1/3)))/12, oo), Interval.Ropen(-sqrt(6)*sqrt(-2^(2/3)*(97 + 9*sqrt(717))^(1/3) + 8 + 46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 36*sqrt(6)/sqrt(-46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 4 + 2^(2/3)*(97 + 9*sqrt(717))^(1/3)))/12 + sqrt(6)*sqrt(-46*2^(1/3)/(97 + 9*sqrt(717))^(1/3) + 4 + 2^(2/3)*(97 + 9*sqrt(717))^(1/3))/12 + 1, 2))
Respuesta rápida [src] 
  /                         /                                                                                      _________________________________________________________________________________________________________________________            \     /                                                                                      _________________________________________________________________________________________________________________________             \\
  |                         |                                                                                     /            _______________                                                                                                          |     |                                                                                     /            _______________                                                                                                           ||
  |                         |                                                                                    /            /         _____                                                                                                           |     |                                                                                    /            /         _____                                                                                                            ||
  |                         |                                                                                   /   4        /   97   \/ 717                                    6                                              23                       |     |                                                                                   /   4        /   97   \/ 717                                    6                                              23                        ||
  |                         |                                                                                  /    - - 2*3 /   --- + -------  + ---------------------------------------------------------------- + -----------------------             |     |                                                                                  /    - - 2*3 /   --- + -------  + ---------------------------------------------------------------- + -----------------------              ||
  |                         |              ______________________________________________________             /     3     \/    432      48                ______________________________________________________           _______________             |     |              ______________________________________________________             /     3     \/    432      48                ______________________________________________________           _______________              ||
  |                         |             /            _______________                                       /                                            /            _______________                                     /         _____              |     |             /            _______________                                       /                                            /            _______________                                     /         _____               ||
  |                         |            /            /         _____                                       /                                            /            /         _____                                     /   97   \/ 717               |     |            /            /         _____                                       /                                            /            /         _____                                     /   97   \/ 717                ||
  |                         |           /   2        /   97   \/ 717                23                     /                                            /   2        /   97   \/ 717                23              18*3 /   --- + -------              |     |           /   2        /   97   \/ 717                23                     /                                            /   2        /   97   \/ 717                23              18*3 /   --- + -------               ||
  |                         |          /    - + 2*3 /   --- + -------  - -----------------------          /                                            /    - + 2*3 /   --- + -------  - -----------------------       \/    432      48                |     |          /    - + 2*3 /   --- + -------  - -----------------------          /                                            /    - + 2*3 /   --- + -------  - -----------------------       \/    432      48                 ||
  |                         |         /     3     \/    432      48              _______________         /                                            /     3     \/    432      48              _______________                                        |     |         /     3     \/    432      48              _______________         /                                            /     3     \/    432      48              _______________                                         ||
  |                         |        /                                          /         _____         /                                            /                                          /         _____                                         |     |        /                                          /         _____         /                                            /                                          /         _____                                          ||
  |                         |       /                                          /   97   \/ 717         /                                            /                                          /   97   \/ 717                                          |     |       /                                          /   97   \/ 717         /                                            /                                          /   97   \/ 717                                           ||
  |                         |      /                                     18*3 /   --- + -------       /                                            /                                     18*3 /   --- + -------                                         |     |      /                                     18*3 /   --- + -------       /                                            /                                     18*3 /   --- + -------                                          ||
  |                         |    \/                                         \/    432      48       \/                                           \/                                         \/    432      48                                           |     |    \/                                         \/    432      48       \/                                           \/                                         \/    432      48                                            ||
Or|And(-oo < x, x < -1), And|1 + ---------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------- <= x, x < 2|, And|1 + ---------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------- <= x, x < oo||
  \                         \                                   2                                                                                                      2                                                                                /     \                                   2                                                                                                      2                                                                                 //
(−∞<x∧x<−1)∨(−−297432+717483+43+231897432+717483+6−231897432+717483+23+297432+7174832+−231897432+717483+23+297432+7174832+1≤x∧x<2)∨(−231897432+717483+23+297432+7174832+1+−297432+717483+43+231897432+717483+6−231897432+717483+23+297432+7174832≤x∧x<∞)\left(-\infty < x \wedge x < -1\right) \vee \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}} + \frac{4}{3} + \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{6}{\sqrt{- \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}}}}}{2} + \frac{\sqrt{- \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}}}{2} + 1 \leq x \wedge x < 2\right) \vee \left(\frac{\sqrt{- \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}}}{2} + 1 + \frac{\sqrt{- 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}} + \frac{4}{3} + \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{6}{\sqrt{- \frac{23}{18 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}} + \frac{2}{3} + 2 \sqrt[3]{\frac{97}{432} + \frac{\sqrt{717}}{48}}}}}}{2} \leq x \wedge x < \infty\right) 
((-oo < x)∧(x < -1))∨((x < 2)∧(1 + sqrt(2/3 + 2*(97/432 + sqrt(717)/48)^(1/3) - 23/(18*(97/432 + sqrt(717)/48)^(1/3)))/2 - sqrt(4/3 - 2*(97/432 + sqrt(717)/48)^(1/3) + 6/sqrt(2/3 + 2*(97/432 + sqrt(717)/48)^(1/3) - 23/(18*(97/432 + sqrt(717)/48)^(1/3))) + 23/(18*(97/432 + sqrt(717)/48)^(1/3)))/2 <= x))∨((x < oo)∧(1 + sqrt(2/3 + 2*(97/432 + sqrt(717)/48)^(1/3) - 23/(18*(97/432 + sqrt(717)/48)^(1/3)))/2 + sqrt(4/3 - 2*(97/432 + sqrt(717)/48)^(1/3) + 6/sqrt(2/3 + 2*(97/432 + sqrt(717)/48)^(1/3) - 23/(18*(97/432 + sqrt(717)/48)^(1/3))) + 23/(18*(97/432 + sqrt(717)/48)^(1/3)))/2 <= x))
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