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If a^x=b^y=c^z\ a n d\ b^2=a c , prove t...

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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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. 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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  2. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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

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

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

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

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

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  9. Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13)

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  10. Prove that: (sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ ...

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  11. Prove that: 9^(3/2\ )-\ 3\ xx\ 5^0-\ (1/(81))^(-1/2)=15

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  12. Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

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  13. Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...

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  14. Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...

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  15. Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...

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  16. Prove that: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ x...

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  17. Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1...

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  18. Solve: 1/(1+x^(a-b))+1/(1+x^(b-a))=?

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  19. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

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  20. Solve the following equation - (i) 2^(x+1)=8

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