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2(log(x)/log(3))+(log(27x+(1/x^2))/log(3))>=2((log(((3x^2)+x))/sqrt(2))/log(3))+2 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                               /   /   2    \\    
              /       1 \      |log\3*x  + x/|    
           log|27*x + --|      |-------------|    
              |        2|      |      ___    |    
  log(x)      \       x /      \    \/ 2     /    
2*------ + -------------- >= 2*--------------- + 2
  log(3)       log(3)               log(3)        
$$2 \frac{\log{\left(x \right)}}{\log{\left(3 \right)}} + \frac{\log{\left(27 x + \frac{1}{x^{2}} \right)}}{\log{\left(3 \right)}} \geq 2 \frac{\frac{1}{\sqrt{2}} \log{\left(3 x^{2} + x \right)}}{\log{\left(3 \right)}} + 2$$
2*(log(x)/log(3)) + log(27*x + 1/(x^2))/log(3) >= 2*((log(3*x^2 + x)/sqrt(2))/log(3)) + 2
Solución de la desigualdad en el gráfico