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log(2)*x+1>log(4)*x^2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                       2
log(2)*x + 1 > log(4)*x 
$$x \log{\left(2 \right)} + 1 > x^{2} \log{\left(4 \right)}$$
x*log(2) + 1 > x^2*log(4)
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
   /          ____________        ____________    \
   |    1   \/ 8 + log(2)   1   \/ 8 + log(2)     |
And|x < - + --------------, - - -------------- < x|
   |    4        ________   4        ________     |
   \         4*\/ log(2)         4*\/ log(2)      /
$$x < \frac{1}{4} + \frac{\sqrt{\log{\left(2 \right)} + 8}}{4 \sqrt{\log{\left(2 \right)}}} \wedge - \frac{\sqrt{\log{\left(2 \right)} + 8}}{4 \sqrt{\log{\left(2 \right)}}} + \frac{1}{4} < x$$
(x < 1/4 + sqrt(8 + log(2))/(4*sqrt(log(2))))∧(1/4 - sqrt(8 + log(2))/(4*sqrt(log(2))) < x)
Respuesta rápida 2 [src]
       ____________        ____________ 
 1   \/ 8 + log(2)   1   \/ 8 + log(2)  
(- - --------------, - + --------------)
 4        ________   4        ________  
      4*\/ log(2)         4*\/ log(2)   
$$x\ in\ \left(- \frac{\sqrt{\log{\left(2 \right)} + 8}}{4 \sqrt{\log{\left(2 \right)}}} + \frac{1}{4}, \frac{1}{4} + \frac{\sqrt{\log{\left(2 \right)} + 8}}{4 \sqrt{\log{\left(2 \right)}}}\right)$$
x in Interval.open(-sqrt(log(2) + 8)/(4*sqrt(log(2))) + 1/4, 1/4 + sqrt(log(2) + 8)/(4*sqrt(log(2))))