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

En la desigualdad la incógnita

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 / 
log(5x)2log(2)xlog(5x)log(12)+x2log((x5)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(\sqrt{\frac{1}{2}} \right)}} + \frac{x^{2} \log{\left(\left(x - 5\right)^{2} \right)}}{\log{\left(2 \right)}}
log(5 - x)^2/log(sqrt(2)) >= (x*log(5 - x))/log(sqrt(1/2)) + (x^2*log((x - 5)^2))/log(2)