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If x=2^(1/3)+\ 2^(2/3) show that x^3-...

If `x=2^(1/3)+\ 2^(2/3)` show that `x^3-6x=6`

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RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Find the value of x in each of the following: 2^(x-7)\ xx\ 5^(x-4)=125...

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  2. Find the value of x in each of the following: (i)\ 5^(2x+3)=1 (ii)\ ...

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  3. If x=2^(1/3)+\ 2^(2/3) show that x^3-6x=6

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  4. Determine (8x)^x , if 9^(x+2)=240+9^x

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  5. If 3^(x+1)=9^(x-2), find the value of 2^(1+x)

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  6. If 3^(4x)=(81)^(-1) and 10^(1/y)=0. 0001 , find the value of 2^(-x+4y)

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  7. If 5^(3x)=\ 125\ and 10^y=0. 001 find x\ a n d\ y

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  8. Solve the following equations: (i)\ 3^(x+1)=27\ xx\ 3^4 \ and (ii) (...

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  9. If a and b are distinct positive primes such that root(3)(a^6b^(-4))...

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  10. If a\ a n d\ b are different positive primes such that (i)\ ((a^(-1)\ ...

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  11. If 2^x\ 3^y\ 5^z=2160\ , find x ,\ y\ a n d\ z . Hence, compute the va...

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  12. If 1176=2^a xx\ 3^bxx\ 7^c , find the values of a ,\ b\ a n d\ c . Hen...

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  13. Simplify: (i)\ ((x^(a+b))/(x^c))^(a-b)\ ((x^(b+c))/(x^a))^(b-c)\ ((x^...

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  14. Show that: ((a+1/b)^m xx\ (a-1/b)^n)/((b+1/a)^m\ xx\ (b-1/a)^n)=(a/b)^...

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  15. If a=x^(m+n)\ y^l,\ b=x^(n+l)\ y^m and c=x^(l+m)y^n , prove that a^(m-...

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  16. If x=a^(m+n),\ y=a^(n+l) and z=a^(l+m) , prove that x^m y^n z^l=x^n y^...

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  17. Write (625)^(-1/4) in decimal form

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  18. State the product law of exponents.

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  19. State the power law of exponents

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  20. For any positive real number x , find the value of ((x^a)/(x^b))^(a+b)...

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