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RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
- Solve the equation: 3(2^x+1)-2^(x+2)+5=0
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- 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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- 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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- If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1
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- 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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- Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...
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- Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...
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- Assuming that x ,\ y ,\ z are positive real numbers, simplify each of ...
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- Simplify: (i)\ (16^(-1/5))^(5/2) (ii)\ (32)^(-3/5) (iii)\ (343...
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- Simplify: (i)\ (0. 001)^(1/3) (ii)\ ((25)^(3/2)\ xx\ (243)^(3/5))/...
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- Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13) (ii)\ ((5^(-1...
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- Prove that: (sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ ...
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- Prove that: 9^(3/2\ )-\ 3\ xx\ 5^0-\ (1/(81))^(-1/2)=15
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- Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3
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- Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...
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- Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...
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- Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...
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- Prove that: (3^(-3) xx 6^2xx sqrt(98))/(5^2 xx root(3)(1/(25)) xx (15)...
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- Prove that: ((0. 6)^0- (0. 1)^(-1))/((3/8)^(-1) (3/2)^3+ (-1/3)^(-1))=...
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- 1/(1+x^(a-b))+1/(1+x^(b-a))=?
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