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log(1/2)(x^2-4)>log(1/2)(x+2)-1

log(1/2)(x^2-4)>log(1/2)(x+2)-1 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
         / 2    \                       
log(1/2)*\x  - 4/ > log(1/2)*(x + 2) - 1
$$\left(x^{2} - 4\right) \log{\left(\frac{1}{2} \right)} > \left(x + 2\right) \log{\left(\frac{1}{2} \right)} - 1$$
(x^2 - 4)*log(1/2) > (x + 2)*log(1/2) - 1
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
   /          _______________        _______________    \
   |    1   \/ 4 + 25*log(2)   1   \/ 4 + 25*log(2)     |
And|x < - + -----------------, - - ----------------- < x|
   |    2          ________    2          ________      |
   \           2*\/ log(2)            2*\/ log(2)       /
$$x < \frac{1}{2} + \frac{\sqrt{4 + 25 \log{\left(2 \right)}}}{2 \sqrt{\log{\left(2 \right)}}} \wedge - \frac{\sqrt{4 + 25 \log{\left(2 \right)}}}{2 \sqrt{\log{\left(2 \right)}}} + \frac{1}{2} < x$$
(x < 1/2 + sqrt(4 + 25*log(2))/(2*sqrt(log(2))))∧(1/2 - sqrt(4 + 25*log(2))/(2*sqrt(log(2))) < x)
Respuesta rápida 2 [src]
       _______________        _______________ 
 1   \/ 4 + 25*log(2)   1   \/ 4 + 25*log(2)  
(- - -----------------, - + -----------------)
 2          ________    2          ________   
        2*\/ log(2)            2*\/ log(2)    
$$x\ in\ \left(- \frac{\sqrt{4 + 25 \log{\left(2 \right)}}}{2 \sqrt{\log{\left(2 \right)}}} + \frac{1}{2}, \frac{1}{2} + \frac{\sqrt{4 + 25 \log{\left(2 \right)}}}{2 \sqrt{\log{\left(2 \right)}}}\right)$$
x in Interval.open(-sqrt(4 + 25*log(2))/(2*sqrt(log(2))) + 1/2, 1/2 + sqrt(4 + 25*log(2))/(2*sqrt(log(2))))
Gráfico
log(1/2)(x^2-4)>log(1/2)(x+2)-1 desigualdades