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Which of the following conditions necess...

Which of the following conditions necessarily imply that the real number x is rational, I `x^2` is rational II `x^3`and `x^5`are rational III `x^2`and `x^3` are rational

A

I and II only

B

I and III only

C

II and III only

D

III only

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The correct Answer is:
C
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VIKAS GUPTA (BLACK BOOK) ENGLISH-LOGARITHMS -Exercise-5 : Subjective Type Problems
  1. Which of the following conditions necessarily imply that the real numb...

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  2. The number N=6^(log(10)40). 5^(log(10)36) is a natural number ,Then su...

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  3. The minimum value of 'c' such that log(b)(a^(log(2)b))=log(a)(b^(log(2...

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  4. How many positive integers b have the property that log(b)729 is a pos...

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  5. The number of negative integral values of x satisfying the inequality ...

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  6. (6)/(5)a^((log(a)x)(log(10)a)(log(a)5))-3^(log(10)((x)/(10)))=9^(log(1...

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  7. If log(5)((a+b)/(3))=(log(5)a+log(5)b)/(2),"then" (a^(4)+b^(4))/(a^(2...

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  8. Let a , b , c , d be positive integers such that (log)a b=3/2a n d(log...

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  9. The number of real values of x satisfying the equation log(10) sqrt(...

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  10. The ordered pair (x,y) satisfying the equation x^(2)=1+6 log(4)y and...

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  11. If log(7)log(7) sqrt(7sqrt(7sqrt(7)))=1-a log(7)2 and log(15)log(15) s...

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  12. The number of ordered pair(s) of (x, y) satisfying the equations log...

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  13. If log(b) n = 2 and og(n) 2b = 2, then find the value of b.

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  14. If log(y) x + log(x) y = 2, x^(2)+y = 12 , then the value of xy is

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  15. If x, y satisfy the equation, y^(x)=x^(y) and x=2y, then x^(2)+y^(2)=

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  16. Find the number of real values of x satisfying the equation. log(2)(...

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  17. If x(1), x(2)(x(1) gt x(2)) are the two solutions of the equation 3^...

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  18. Find the number or real values of x satisfying the equation 9^(2log(9)...

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  19. If log(16)(log(root(4)(3))(log(root(3)(5))(x)))=(1)/(2), find x.

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  20. The value [(1)/(6)((2log(10)(1728))/(1+(1)/(2)log(10)(0.36)+(1)/(3)log...

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