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If a != 1 and l n a^(2) + (l n a^(2))^(2...

If `a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 (l n a + (l n a)^(2) + ( ln a)^(3) + (l n a)^(4) + ....)` then 'a' is equal to

A

`e^(1//5)`

B

`sqrte`

C

`root(3)(e)`

D

`root(4)(e)`

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The correct Answer is:
D
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ALLEN-SEQUENCE AND PROGRESSION-Exercise O-2
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  7. Let an, n in N is an A.P with common difference d and all whose terms ...

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  9. The arithmetic mean of the nine number in the given set {9,99,999, ......

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  11. If a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 ...

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  12. The sum of the first three terms of an increasing G.P. is 21 and the s...

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  13. a, b, c are distinct positive real in HP, then the value of the expres...

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  14. If sin(x-y),sinx,sin(x+y) are in H.P., then find the value of sinxsec(...

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  15. An H.M. is inserted between the number 1/3 and an unknown number. If w...

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  16. lf abcd=1 where a,b,c,d are positive reals then the minimum value of ...

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  17. If 27 abc> (a+b+c)^3 and 3a +4b +5c=12 then 1/a^2+1/b^3+1/c^5=10, wh...

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  18. If x = sum(n=0)^(oo) a^(n), y=sum(n=0)^(oo) b^(n), z = sum(n=0)^(oo) ...

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  19. IF S=1^2+3^2+5^2....99^2 then the value of the sum 2^2+4^2+6^2...100^2

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  20. For which positive integers n is the ratio, (sum+(k=1)^(n) k^(2))/(sum...

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