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If log(y) x + log(x) y = 2, x^(2)+y = 12...

If `log_(y) x + log_(x) y = 2, x^(2)+y = 12` , then the value of xy is

A

9

B

12

C

15

D

21

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` t=log_(y) x(x, y gt 0, and ne 1)," then " t+1/t = 2 or (t-1)^(2) = 0`
` :. T = log_(y) x = 1 , i.e., x = y `.We get
` x^(2) + x - 12 = 0 x = -4, 3`.
x = 3 only (-4 rejected)
` :. Y = 3`,
` :. X = 9`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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  3. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

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  4. সমাধান করো : 4^(log9 3)+9^(log2 4)=10^(logx 83)।

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  5. Solve (x+1)^(log(10) (x+1))=100(x+1)

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  6. If log2x+logx2=10/3=log2y+logy2 and x!=y ,then x+y=

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  7. If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...

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  8. If (log)3{5+4(log)3(x-1)}=2, then x is equal to

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  9. If 2x^((log)4 3)+3^((log)4x)=27 , then x is equal to 2 (b) 4 (c) 8 (d...

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  10. The equation log4(3-x)+log(0.25)(3+x)=log4(1-x)+log(0.25)(2x+1) has

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  11. The value of b for which the equation 2(log)(1/(25))(b x+28)=-(log)5(1...

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  12. If the equation 2^x(1-2^x)+4^y=2^y is solved for y in terms of x where...

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  13. Solve the equation x^(logx(x+3)^2 )=16

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  14. The product of roots of the equation (log(8)(8//x^(2)))/((log(8)x)^(2)...

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

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

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

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

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

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

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