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

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

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. 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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  2. If x=3,\ find the value of (x^(1/3)+\ x^(-1/3))\ (x^(2/3)+x^(-2/3)-1\...

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

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

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

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

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

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  8. 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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  9. 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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  10. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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

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

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

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

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

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

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

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

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

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