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log(5)(2-2/x)-log(5)(x-3)>=log(5)(x+3/x^2) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src]
       /    2\                            /    3 \
log(5)*|2 - -| - log(5)*(x - 3) >= log(5)*|x + --|
       \    x/                            |     2|
                                          \    x /
$$\left(2 - \frac{2}{x}\right) \log{\left(5 \right)} - \left(x - 3\right) \log{\left(5 \right)} \geq \left(x + \frac{3}{x^{2}}\right) \log{\left(5 \right)}$$
(2 - 2/x)*log(5) - (x - 3)*log(5) >= (x + 3/x^2)*log(5)
Solución de la desigualdad en el gráfico
Respuesta rápida [src]
                                         ________________
                                        /           ____ 
                                       /  127   9*\/ 43  
                                    3 /   --- + -------- 
     5              13              \/     8       4     
x <= - - ------------------------ - ---------------------
     6           ________________             3          
                /           ____                         
               /  127   9*\/ 43                          
         12*3 /   --- + --------                         
            \/     8       4                             
$$x \leq - \frac{\sqrt[3]{\frac{9 \sqrt{43}}{4} + \frac{127}{8}}}{3} - \frac{13}{12 \sqrt[3]{\frac{9 \sqrt{43}}{4} + \frac{127}{8}}} + \frac{5}{6}$$
x <= -(9*sqrt(43)/4 + 127/8)^(1/3)/3 - 13/(12*(9*sqrt(43)/4 + 127/8)^(1/3)) + 5/6
Respuesta rápida 2 [src]
                                      _________________ 
                                   3 /            ____  
      5             13             \/  127 + 18*\/ 43   
(-oo, - - ---------------------- - --------------------]
      6        _________________            6           
            3 /            ____                         
          6*\/  127 + 18*\/ 43                          
$$x\ in\ \left(-\infty, - \frac{\sqrt[3]{18 \sqrt{43} + 127}}{6} - \frac{13}{6 \sqrt[3]{18 \sqrt{43} + 127}} + \frac{5}{6}\right]$$
x in Interval(-oo, -(18*sqrt(43) + 127)^(1/3)/6 - 13/(6*(18*sqrt(43) + 127)^(1/3)) + 5/6)