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log(3-x)-log((sqrt2/2)/(5-x))>1/2+log(x+7) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                //  ___\\                   
                ||\/ 2 ||                   
                ||-----||                   
                |\  2  /|                   
log(3 - x) - log|-------| > 1/2 + log(x + 7)
                \ 5 - x /                   
$$- \log{\left(\frac{\frac{1}{2} \sqrt{2}}{5 - x} \right)} + \log{\left(3 - x \right)} > \log{\left(x + 7 \right)} + \frac{1}{2}$$
-log((sqrt(2)/2)/(5 - x)) + log(3 - x) > log(x + 7) + 1/2
Respuesta rápida 2 [src]
                  _______________________              
           ___   /              ___  1/2      ___  1/2 
         \/ 2 *\/  8 + E + 44*\/ 2 *e       \/ 2 *e    
(-7, 4 - -------------------------------- + ----------)
                        4                       4      
$$x\ in\ \left(-7, - \frac{\sqrt{2} \sqrt{e + 8 + 44 \sqrt{2} e^{\frac{1}{2}}}}{4} + \frac{\sqrt{2} e^{\frac{1}{2}}}{4} + 4\right)$$
x in Interval.open(-7, -sqrt(2)*sqrt(E + 8 + 44*sqrt(2)*exp(1/2))/4 + sqrt(2)*exp(1/2)/4 + 4)
Respuesta rápida [src]
   /                         _______________________             \
   |                  ___   /              ___  1/2      ___  1/2|
   |                \/ 2 *\/  8 + E + 44*\/ 2 *e       \/ 2 *e   |
And|-7 < x, x < 4 - -------------------------------- + ----------|
   \                               4                       4     /
$$-7 < x \wedge x < - \frac{\sqrt{2} \sqrt{e + 8 + 44 \sqrt{2} e^{\frac{1}{2}}}}{4} + \frac{\sqrt{2} e^{\frac{1}{2}}}{4} + 4$$
(-7 < x)∧(x < 4 - sqrt(2)*sqrt(8 + E + 44*sqrt(2)*exp(1/2))/4 + sqrt(2)*exp(1/2)/4)