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Simplify : (i) log(1/(sqrtx) )(y) xx l...

Simplify :
(i) `log_(1/(sqrtx) )(y) xx log_(1/(root(3)(y)))(z) xx log_(1/(root(4)(z)))(x)`

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The correct Answer is:
`-24`
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CALCUTTA BOOK HOUSE-LOGARITHM-Exercise - 7 (Long-answer type questions)
  1. Calculate : (v) 1/6 sqrt((3log 1728)/(1+1/2 log 0.36 + 1/3log8))

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  2. Calculate : (vi) log(2)5 xx log(6)16 xx log(5) 8 xx log(8)6.

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  3. Simplify : (i) log(1/(sqrtx) )(y) xx log(1/(root(3)(y)))(z) xx log(1...

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  4. Simplify : (ii) 23 log 16/15 + 17log 25/24 + 10log 81/80

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  5. Simplify : (iii) 3log((36)/(25))+log((6)/(27))^(3)-2log((16)/(125))

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  6. Prove that log2+16log (16/15)+12log(25/24)+7log(81/80)=1

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  7. If log(40)4 = a and log(40)5 = b, then show that log(40)16=4(1-a-b).

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  8. If log(6)15 = alpha, log(12)18= beta and log(25)24 = gamma, then prove...

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  9. If log(12)18 = x and log(24)54 = y, then show that xy + 5(x-y) = 1

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  10. If log(a)M = (logb M) xx P, then express P in terms of a and b.

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  11. If 1/2 log(3)M + 3log(3)N = 1, then express M in terms of N.

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  12. Prove that 1/(log2 pi) + 1/(log(6)pi) > 2.

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  13. Prove that the value of log(10)3 lies in between 1/2 and 2/5.

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  14. Prove that the value of log(20)3 lies in between 1/2 and 1/3.

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  15. Prove that : (i) log(1^(1/5)+32^(1/5)+243^(1/5))=1/5(log1 + log 32 +...

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  16. Prove that : (ii) log(1+2+3) = log1 + log2 + log3.

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  17. Prove that : (iii) (yz)^(log(y/z))(zx)^(log(z/x))(xy)^(log(x/y)) = 1

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  18. Prove that : (iv) a^(log(a^2)x) xx b^(log(b^2)y) xx c^(log(c^2)z) = ...

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  19. Prove that : (v) p^(log(x)q) = q^(log(x)p)

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  20. Prove that : (vi) log(a)x + log(a^2)x^(2) + log(a^3)x^(3) + ………….+ l...

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