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If (log)2x+(log)2ygeq6, then the least v...

If `(log)_2x+(log)_2ygeq6,` then the least value of `x+y` is 4 (b) 8 (d) 16 (d) 32

A

4

B

8

C

16

D

32

Text Solution

Verified by Experts

The correct Answer is:
C
Given ` log_(2) x + log_(2) y ge 6`
` rArr log_(2) (xy) ge 6`
` rArr xy ge 64`
Also to define ` log_(2) x and log_(2) y `, we have
` x gt 0, y gt 0`.
Since A.M.` ge G.M., `we have
` (x+y)/2 ge sqrt(xy)`
` or x + y ge 2 sqrt(xy) ge 16`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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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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