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log(5-x)^2/log(sqrt(2))>=x^2*log(x-5)^2/log(2)+x*log(5-x)/log(1/sqrt(2)) desigualdades

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Solución

Ha introducido [src]
   2            2    2                      
log (5 - x)    x *log (x - 5)   x*log(5 - x)
----------- >= -------------- + ------------
    /  ___\        log(2)           /  1  \ 
 log\\/ 2 /                      log|-----| 
                                    |  ___| 
                                    \\/ 2 / 
$$\frac{\log{\left(5 - x \right)}^{2}}{\log{\left(\sqrt{2} \right)}} \geq \frac{x \log{\left(5 - x \right)}}{\log{\left(\frac{1}{\sqrt{2}} \right)}} + \frac{x^{2} \log{\left(x - 5 \right)}^{2}}{\log{\left(2 \right)}}$$
log(5 - x)^2/log(sqrt(2)) >= (x*log(5 - x))/log(1/(sqrt(2))) + (x^2*log(x - 5)^2)/log(2)