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The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).
(The answer is :0 ) .
solve?
(The answer is :0 ) .
solve?
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The number of real inequalities of a for the the following inequality ...
Number of Real Inequalities for the Given Inequality
In order for the inequality log(x^2 - 4x + a) base x > 0 to hold for all real values of x in the interval (0,1), we must consider the conditions under which the logarithmic function is defined and positive.
Logarithmic Function Definition
For the logarithmic function log(x) to be defined, the argument x must be greater than 0. In this case, the argument is x^2 - 4x + a. Therefore, we must have x^2 - 4x + a > 0 for the inequality to be valid.
Quadratic Inequality Analysis
The quadratic inequality x^2 - 4x + a > 0 represents a parabola that opens upwards. The discriminant of this quadratic is 4^2 - 4*a = 16 - 4a. For the parabola to be above the x-axis, the discriminant must be negative, i.e., 16 - 4a < />
Determining the Number of Real Solutions
Solving the inequality 16 - 4a < 0,="" we="" get="" a="" /> 4. This means that for the given inequality log(x^2 - 4x + a) base x > 0 to hold for all real values of x in the interval (0,1), the constant term a must be greater than 4.
Conclusion: Number of Real Inequalities
Since a must be greater than 4 for the inequality to be valid, there are no real inequalities of a that satisfy the given conditions. Therefore, the number of real inequalities for the given inequality is 0.
In order for the inequality log(x^2 - 4x + a) base x > 0 to hold for all real values of x in the interval (0,1), we must consider the conditions under which the logarithmic function is defined and positive.
Logarithmic Function Definition
For the logarithmic function log(x) to be defined, the argument x must be greater than 0. In this case, the argument is x^2 - 4x + a. Therefore, we must have x^2 - 4x + a > 0 for the inequality to be valid.
Quadratic Inequality Analysis
The quadratic inequality x^2 - 4x + a > 0 represents a parabola that opens upwards. The discriminant of this quadratic is 4^2 - 4*a = 16 - 4a. For the parabola to be above the x-axis, the discriminant must be negative, i.e., 16 - 4a < />
Determining the Number of Real Solutions
Solving the inequality 16 - 4a < 0,="" we="" get="" a="" /> 4. This means that for the given inequality log(x^2 - 4x + a) base x > 0 to hold for all real values of x in the interval (0,1), the constant term a must be greater than 4.
Conclusion: Number of Real Inequalities
Since a must be greater than 4 for the inequality to be valid, there are no real inequalities of a that satisfy the given conditions. Therefore, the number of real inequalities for the given inequality is 0.
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The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve?
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The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve?.
The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of real inequalities of a for the the following inequality log( x^2-4x+a) base x >0 holds for all real values of x in the interval (0,1).(The answer is :0 ) .solve?.
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