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log2((x-1)(x^2+3))<=log2(4x-x^2-3)+log2(5-x) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
   /        / 2    \\       /       2    \             
log\(x - 1)*\x  + 3//    log\4*x - x  - 3/   log(5 - x)
--------------------- <= ----------------- + ----------
        log(2)                 log(2)          log(2)  
$$\frac{\log{\left(\left(x - 1\right) \left(x^{2} + 3\right) \right)}}{\log{\left(2 \right)}} \leq \frac{\log{\left(5 - x \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(\left(- x^{2} + 4 x\right) - 3 \right)}}{\log{\left(2 \right)}}$$
log((x - 1)*(x^2 + 3))/log(2) <= log(5 - x)/log(2) + log(-x^2 + 4*x - 3)/log(2)