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The number of real values of the paramet...

The number of real values of the parameter `k` for which `(log_(16)x)^2-(log)_(16)x+(log)_(16)k=0` with real coefficients will have exactly one solution is 2 (b) 1 (c) 4 (d) none of these

A

2

B

1

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
` log_(16) x = (1 pm sqrt(1-4 log _(16) k))/2`
For exactly one solution, ` 4 log_(16) k = 1`.
` rArr k^(4) = 16, i.e., k=2, -2`.
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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  3. The product of roots of the equation (log(8)(8//x^(2)))/((log(8)x)^(2)...

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  4. Let agt1 be a real number . If S is the set of real number x that are...

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  5. The number of roots of the equation (log)(3sqrt("x"))x+(log)(3x)sqrt(x...

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  6. The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...

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  7. Number of real values of x satisfying the equation (log)2(x^2-x)(log)...

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  8. If xy^(2) = 4 and log(3) (log(2) x) + log(1//3) (log(1//2) y)=1 , then...

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  9. If x1a n dx2 are the roots of the equation e^2 x^(lnx)=x^3 with x1> x2...

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  10. The number of real values of the parameter k for which (log(16)x)^2-(l...

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  11. x^((log)5x)>5 implies x in (0,oo) (b) [2,2.5] (c) (2,2.5) (d) (0,2...

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  12. If S={x in N :2+(log)2sqrt(x+1)>1-(log)(1/2)sqrt(4-x^2)} , then S={1...

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  13. If S={x in R :((log)(0. 6)0. 216)(log)5(5-2x)lt=0}, then S is equal t...

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  14. Solution set of the inequality 1/(2^x-1)>1/(1-2^(x-1)) is 1,oo) (b) 0...

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  15. If (log)2x+(log)2ygeq6, then the least value of x+y is 4 (b) 8 (d...

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  16. Which of the following is a solution of (logx)(5/2-1/x) gt (5/2-1/x) ?

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  17. The solution set of the inequality (log)(10)(x^2-16)lt=(log)(10)(4x-11...

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  18. Solution set of the inequality (log)(0. 8)((log)6(x^2+x)/(x+4))<0 is

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  19. Which of the following is not the solution of (log)3(x^2-2)<(log)3(3/2...

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  20. The true solution set of inequality (log)((x+1))(x^2-4)>1 is equal to ...

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