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Resolver desigualdades/ 8/(log2(16x))>=3/(log2(8x))+1/(log2(2x))

8/(log2(16x))>=3/(log2(8x))+1/(log2(2x)) desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
     8             3            1     
----------- >= ---------- + ----------
/log(16*x)\    /log(8*x)\   /log(2*x)\
|---------|    |--------|   |--------|
\  log(2) /    \ log(2) /   \ log(2) /
$$\frac{8}{\frac{1}{\log{\left(2 \right)}} \log{\left(16 x \right)}} \geq \frac{3}{\frac{1}{\log{\left(2 \right)}} \log{\left(8 x \right)}} + \frac{1}{\frac{1}{\log{\left(2 \right)}} \log{\left(2 x \right)}}$$ 
8/((log(16*x)/log(2))) >= 3/((log(8*x)/log(2))) + 1/(log(2*x)/log(2))
Solución de la desigualdad en el gráfico
Respuesta rápida 2 [src] 
                       ___                
                     \/ 2                 
{0} U (1/16, 1/8) U [-----, 1/2) U [1, oo)
                       8
$$x\ in\ \left\{0\right\} \cup \left(\frac{1}{16}, \frac{1}{8}\right) \cup \left[\frac{\sqrt{2}}{8}, \frac{1}{2}\right) \cup \left[1, \infty\right)$$ 
x in Union(FiniteSet(0), Interval.open(1/16, 1/8), Interval(1, oo), Interval.Ropen(sqrt(2)/8, 1/2))
Respuesta rápida [src] 
  /                           /  ___              \               \
  |                           |\/ 2               |               |
Or|And(1/16 < x, x < 1/8), And|----- <= x, x < 1/2|, x = 0, 1 <= x|
  \                           \  8                /               /
$$\left(\frac{1}{16} < x \wedge x < \frac{1}{8}\right) \vee \left(\frac{\sqrt{2}}{8} \leq x \wedge x < \frac{1}{2}\right) \vee x = 0 \vee 1 \leq x$$ 
(x = 0))∨(1 <= x)∨((1/16 < x)∧(x < 1/8))∨((x < 1/2)∧(sqrt(2)/8 <= x)
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