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Solve the following equations: (i) 2^(x...

Solve the following equations:
(i) `2^(x-5)=256`
(ii) `2^(x+3)=4^(x-1)`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

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  2. Find the value of x , if 5^(x-3)\ 3^(2x-8)=225

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  3. Solve the following equations: (i) 2^(x-5)=256 (ii) 2^(x+3)=4^(x-...

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  4. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

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  5. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

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  6. Solve the equation for x: 5^(2x+1)=6. 5^x-1

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  7. Simplify the following: 3(a^4b^3)^10xx5(a^2b^2)^3

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  8. Simplify that: (2x^(-2)y^3)^3

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  9. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  10. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  11. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  12. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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  13. If a=3\ \ a n d\ b=-2\ , find the values of: (i)\ a^a+b^b (ii)\ a^b+b...

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  14. Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c...

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  15. Prove that: ((x^a)/(x^(b)))^(a^(2+a b+b^2))\ xx\ ((x^b)/(x^(c)))^(b^(2...

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  16. Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

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  17. Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

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  18. Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-...

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  19. Prove that: (a+b+c)/(a^(-1)\ b^(-1)+b^(-1)\ c^(-1)+c^(-1)a^(-1))=a b c

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  20. Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

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