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abs(abs(log3x)-abs(3-x))+abs(3*log3(x)-log9(x^(2*x)))<=(x-3)*log((3^0.5)(x^0.5)) desigualdades

En la desigualdad la incógnita

Solución

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