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if log2 x+ log2 y >= 6 then the least va...

if `log_2 x+ log_2 y >= 6` then the least value of `x+y`

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-LOGARITHM AND ITS PROPERTIES-Exercise (Single)
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  2. The number of solution of x^(log(x)(x+3)^(2)) = 16 is

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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(3sqrtx) x + log(3x) (sqrtx) =0...

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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) gt 1/(1-2^(x-1)) is

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  15. if log2 x+ log2 y >= 6 then the least value of x+y

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  16. Which of the following is not the solution (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) gt 1 is equal t...

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