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How to use it?
- Inequation:
- ((log2(x))^2-2log2(x))^2<11(log2(x))^2-22log2(x)-24
- x^2log625(x+2)≥log5(x^2+4x+4)
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cos(2x)>sqrt(3)/2
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tgx<=1/sqrt(3)
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Identical expressions
- ((log two (x))^ two - two log2(x))^2< eleven (log2(x))^2-22log2(x)- twenty-four
- (( logarithm of 2(x)) squared minus 2 logarithm of 2(x)) squared less than 11( logarithm of 2(x)) squared minus 22 logarithm of 2(x) minus 24
- (( logarithm of two (x)) to the power of two minus two logarithm of 2(x)) squared less than eleven ( logarithm of 2(x)) squared minus 22 logarithm of 2(x) minus twenty minus four
- ((log2(x))2-2log2(x))2<11(log2(x))2-22log2(x)-24
- log2x2-2log2x2<11log2x2-22log2x-24
- ((log2(x))²-2log2(x))²<11(log2(x))²-22log2(x)-24
- ((log2(x)) to the power of 2-2log2(x)) to the power of 2<11(log2(x)) to the power of 2-22log2(x)-24
- log2x^2-2log2x^2<11log2x^2-22log2x-24
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Similar expressions
- ((log2(x))^2-2log2(x))^2<11(log2(x))^2-22log2(x)+24
- ((log2(x))^2+2log2(x))^2<11(log2(x))^2-22log2(x)-24
- ((log2(x))^2-2log2(x))^2<11(log2(x))^2+22log2(x)-24
((log2(x))^2-2log2(x))^2<11(log2(x))^2-22log2(x)-24 inequation
The solution
You have entered
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2 / 2 \ 2 |/log(x)\ log(x)| /log(x)\ log(x) ||------| - 2*------| < 11*|------| - 22*------ - 24 \\log(2)/ log(2)/ \log(2)/ log(2)
$$\left(\left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{2} - 2 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{2} < \left(11 \left(\frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right)^{2} - 22 \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}\right) - 24$$
((log(x)/log(2))^2 - 2*log(x)/log(2))^2 < 11*(log(x)/log(2))^2 - 22*log(x)/log(2) - 24
Solving inequality on a graph
Rapid solution
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Or(And(1/4 < x, x < 1/2), And(8 < x, x < 16))
$$\left(\frac{1}{4} < x \wedge x < \frac{1}{2}\right) \vee \left(8 < x \wedge x < 16\right)$$
((1/4 < x)∧(x < 1/2))∨((8 < x)∧(x < 16))
Rapid solution 2
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(1/4, 1/2) U (8, 16)
$$x\ in\ \left(\frac{1}{4}, \frac{1}{2}\right) \cup \left(8, 16\right)$$
x in Union(Interval.open(1/4, 1/2), Interval.open(8, 16))