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2log(0.5)((x-1)/(x+1/3))+log(0.5)(x+1.3)^2>=2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                                      2     
            x - 1             /    13\      
2*log(1/2)*------- + log(1/2)*|x + --|  >= 2
           x + 1/3            \    10/      
$$\frac{x - 1}{x + \frac{1}{3}} \cdot 2 \log{\left(\frac{1}{2} \right)} + \left(x + \frac{13}{10}\right)^{2} \log{\left(\frac{1}{2} \right)} \geq 2$$
((x - 1)/(x + 1/3))*(2*log(1/2)) + (x + 13/10)^2*log(1/2) >= 2
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
   /                    ______________________________________________________________________________________________________________________________________________________                                                                                                                                                                           \
   |                   /                  _______________________________________________________________________________________                                                                                                                                                                                                                        |
   |                  /                  /                                                                                     2                                                                                                                                                                                                                         |
   |                 /                  /                                  /170368   11*(600 + 1367*log(2))   200 - 431*log(2)\                                                                                                                      1936   600 + 1367*log(2)                                                                            |
   |                /                  /                               3   |------ - ---------------------- + ----------------|                                                                                                                    - ---- + -----------------                                                                            |
   |       44      /       85184      /    /  1936   600 + 1367*log(2)\    \91125         3375*log(2)            300*log(2)   /     200 - 431*log(2)   11*(600 + 1367*log(2))                                                                        2025       900*log(2)                                                                               |
And|x <= - -- + 3 /      - ----- +   /     |- ---- + -----------------|  + -----------------------------------------------------  - ---------------- + ----------------------  - --------------------------------------------------------------------------------------------------------------------------------------------------------------, -1/3 < x|
   |       45   \/         91125   \/      \  2025       900*log(2)   /                              4                                 600*log(2)           6750*log(2)                  ______________________________________________________________________________________________________________________________________________________          |
   |                                                                                                                                                                                    /                  _______________________________________________________________________________________                                                       |
   |                                                                                                                                                                                   /                  /                                                                                     2                                                        |
   |                                                                                                                                                                                  /                  /                                  /170368   11*(600 + 1367*log(2))   200 - 431*log(2)\                                                         |
   |                                                                                                                                                                                 /                  /                               3   |------ - ---------------------- + ----------------|                                                         |
   |                                                                                                                                                                                /       85184      /    /  1936   600 + 1367*log(2)\    \91125         3375*log(2)            300*log(2)   /     200 - 431*log(2)   11*(600 + 1367*log(2))           |
   |                                                                                                                                                                             3 /      - ----- +   /     |- ---- + -----------------|  + -----------------------------------------------------  - ---------------- + ----------------------           |
   \                                                                                                                                                                             \/         91125   \/      \  2025       900*log(2)   /                              4                                 600*log(2)           6750*log(2)                 /
$$x \leq - \frac{44}{45} - \frac{- \frac{1936}{2025} + \frac{600 + 1367 \log{\left(2 \right)}}{900 \log{\left(2 \right)}}}{\sqrt[3]{- \frac{85184}{91125} - \frac{200 - 431 \log{\left(2 \right)}}{600 \log{\left(2 \right)}} + \sqrt{\left(- \frac{1936}{2025} + \frac{600 + 1367 \log{\left(2 \right)}}{900 \log{\left(2 \right)}}\right)^{3} + \frac{\left(- \frac{11 \left(600 + 1367 \log{\left(2 \right)}\right)}{3375 \log{\left(2 \right)}} + \frac{200 - 431 \log{\left(2 \right)}}{300 \log{\left(2 \right)}} + \frac{170368}{91125}\right)^{2}}{4}} + \frac{11 \left(600 + 1367 \log{\left(2 \right)}\right)}{6750 \log{\left(2 \right)}}}} + \sqrt[3]{- \frac{85184}{91125} - \frac{200 - 431 \log{\left(2 \right)}}{600 \log{\left(2 \right)}} + \sqrt{\left(- \frac{1936}{2025} + \frac{600 + 1367 \log{\left(2 \right)}}{900 \log{\left(2 \right)}}\right)^{3} + \frac{\left(- \frac{11 \left(600 + 1367 \log{\left(2 \right)}\right)}{3375 \log{\left(2 \right)}} + \frac{200 - 431 \log{\left(2 \right)}}{300 \log{\left(2 \right)}} + \frac{170368}{91125}\right)^{2}}{4}} + \frac{11 \left(600 + 1367 \log{\left(2 \right)}\right)}{6750 \log{\left(2 \right)}}} \wedge - \frac{1}{3} < x$$
(-1/3 < x)∧(x <= -44/45 + (-85184/91125 + sqrt((-1936/2025 + (600 + 1367*log(2))/(900*log(2)))^3 + (170368/91125 - 11*(600 + 1367*log(2))/(3375*log(2)) + (200 - 431*log(2))/(300*log(2)))^2/4) - (200 - 431*log(2))/(600*log(2)) + 11*(600 + 1367*log(2))/(6750*log(2)))^(1/3) - (-1936/2025 + (600 + 1367*log(2))/(900*log(2)))/(-85184/91125 + sqrt((-1936/2025 + (600 + 1367*log(2))/(900*log(2)))^3 + (170368/91125 - 11*(600 + 1367*log(2))/(3375*log(2)) + (200 - 431*log(2))/(300*log(2)))^2/4) - (200 - 431*log(2))/(600*log(2)) + 11*(600 + 1367*log(2))/(6750*log(2)))^(1/3))