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log2((x-1)(10+3x-x^2))+log2((7-x)/(10+3x-x^2))<=-2+log2(9x) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
                                  /    7 - x    \                 
                               log|-------------|                 
   /        /            2\\      |            2|                 
log\(x - 1)*\10 + 3*x - x //      \10 + 3*x - x /         log(9*x)
---------------------------- + ------------------ <= -2 + --------
           log(2)                    log(2)                log(2) 
$$\frac{\log{\left(\frac{7 - x}{- x^{2} + \left(3 x + 10\right)} \right)}}{\log{\left(2 \right)}} + \frac{\log{\left(\left(x - 1\right) \left(- x^{2} + \left(3 x + 10\right)\right) \right)}}{\log{\left(2 \right)}} \leq \frac{\log{\left(9 x \right)}}{\log{\left(2 \right)}} - 2$$
log((7 - x)/(-x^2 + 3*x + 10))/log(2) + log((x - 1)*(-x^2 + 3*x + 10))/log(2) <= log(9*x)/log(2) - 2