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10^x/(2*(log(x+1)/log(2))^2*(log(x+2)/log(3)))<=((15*3^x)^x)/(9*(log(x+1)/log(2))^2*(log(x+2)/log(3))) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                                              x         
             x                         /    x\          
           10                          \15*3 /          
-------------------------- <= --------------------------
              2                             2           
  /log(x + 1)\  log(x + 2)      /log(x + 1)\  log(x + 2)
2*|----------| *----------    9*|----------| *----------
  \  log(2)  /    log(3)        \  log(2)  /    log(3)  
$$\frac{10^{x}}{2 \left(\frac{\log{\left(x + 1 \right)}}{\log{\left(2 \right)}}\right)^{2} \frac{\log{\left(x + 2 \right)}}{\log{\left(3 \right)}}} \leq \frac{\left(15 \cdot 3^{x}\right)^{x}}{9 \left(\frac{\log{\left(x + 1 \right)}}{\log{\left(2 \right)}}\right)^{2} \frac{\log{\left(x + 2 \right)}}{\log{\left(3 \right)}}}$$
10^x/(((2*(log(x + 1)/log(2))^2)*(log(x + 2)/log(3)))) <= (15*3^x)^x/(((9*(log(x + 1)/log(2))^2)*(log(x + 2)/log(3))))
Solución de la desigualdad en el gráfico