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log(1/x)/log(3)+log(x*x+3*x-9)/log(3)<=log(x*x+3*x+(1/x)-10)/log(3) desigualdades

En la desigualdad la incógnita

Solución

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