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If x , y ,z are positive real numbers sh...

If `x , y ,z` are positive real numbers show that: `sqrt(x^(-1)y)dotsqrt(y^(-1)z)dotsqrt(z^(-1)x)=1`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Assuming that x , y , z are positive real numbers, simplify each of th...

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  2. Assuming that x , y , z are positive real numbers, simplify each of th...

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  3. If x , y ,z are positive real numbers show that: sqrt(x^(-1)y)dotsqrt(...

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  4. If ((x^(-1)y^2)/(x^3y^(-2)))^1.\ ((x^6\ y^(-3))/(x^2\ y^3))^(1/2)=x^a ...

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  5. If x=\ 28^(1/3)\ \ a n d\ y=\ 27^(1/3) find the value of x-y-1/(x^2+x...

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  6. If x=3,\ find the value of (x^(1/3)+\ x^(-1/3))\ (x^(2/3)+x^(-2/3)-1\...

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  7. If 25^(n-1) + 100 = 5^ (2n-1), find the value of n :

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  8. Solve the equation for x : (i)\ 4^(2x)=1/(32) (ii)\ sqrt((3/5)^(1-...

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  9. Solve the equation for x : (5^0+2/3)^2 =(0. 6)^(3-2x)

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  10. Solve the equation for x : 2^3(5^0+3^(2x))=\ 8 8/(27)

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  11. Solve the equation: 3(2^x+1)-2^(x+2)+5=0

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  12. Solve the equations for x\ a n d\ y: 3^x=9\ xx\ 3^y ,\ 8\ xx\ 2^y=4^x

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  13. Solve the equation for x\ a n d\ y (32)^x-:2^(y+1)=1,\ 16^(4-x/2)-8^y...

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

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  15. If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

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  16. Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...

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  17. Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...

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  18. Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...

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  19. Simplify: (i)(32)^(-3/5) (ii) (343)^(-2/3)

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  20. Simplify: (i)\ ((25)^(3/2)\ xx\ (243)^(3/5))/((16)^(5/4)\ xx\ (8)...

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