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If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove ...

If `a^x=b ,\ b^y=c\ a n d\ c^z=a ,` prove that `x y z=1`

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RS AGGARWAL-SURDS AND INDICES-All Questions
  1. The expression ((x+1/y)^a*(x-1/y)^b)/((y+1/x)^a*(y-1/x)^b) reduces to ...

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  2. If a^x=b^y=c^z \ and\ b^2=a c ,\ then\ y equals a. (xz)/(x+z) b. (x z)...

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  3. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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  4. I f2^x=4^y=8^zand(1/(2x)+1/(4y)+1/(6z))=24/7,t h e nz=?7/48 b)48/7c)44...

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  5. Suppose 4^a=5,\ 5^b=6,\ 6^c=7,\ 7^d=8, then the value of a b c d is a...

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  6. If a b c=1, then (1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1)))=? a. 0...

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  7. If a ,\ b ,\ c are positive real numbers, then sqrt(a^(-1)b)\ xx\ sqrt...

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  8. If 3^(x-y)=27, and 3^(x+y) = 243, then x is equal to a. 0 b. 2 c. 4 d....

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  9. If x^y=y^x, then (x/y)^(x//y) is equal to a. x^(y//x) b. x^(x/y-1) c. ...

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  10. If 4^(x+y)=1\ and \ 4^(x-y)=4, then the values of x and y respectively...

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  11. If 2^(2x-1)+4^x=2^(x-1/2)+2^(x+1/2), then x equals a. 1/2 b. 2/3 ...

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  12. If 3^(2x-y)=3^(x+y)=sqrt27 , the value of y is a. 1/2 b. 3/4 c. 1/4 d....

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  13. If 3^x=5^y=45^z , then a. 2/z=1/y-1/x b. 2/y=1/x-1/z c. 2/x=1/z-1/y d....

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  14. Given 2^x=8^(y+1)\ and\ 9^y=3^(x-9) , then the value of x+y is a. 18 b...

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  15. What are the values of x\ and\ y that satisfy the equation2^(0.7x)*3^(...

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  16. Let r be the result of doubling both the base and the exponent of a^b ...

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  17. Which of the following is the greatest? a. sqrt(2) b. root(3)3 c. root...

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  18. The greatest of sqrt(2),root(6)3,root(3)4,root(4)5 is a. sqrt(2) b. ro...

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  19. The largest number in the sequence 1,\ 2^(1/2),\ 3^(1/3),\ 4^(1/4),\.....

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  20. If x=5+2sqrt(6), then (x-1)/sqrt(x) is equal to a. sqrt(2) b. sqrt(3) ...

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