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If x, y, z be three consecutive intergers, then prove that `log(1+xz) = 2 log y`

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CALCUTTA BOOK HOUSE-LOGARITHM-Examples (Long-answer type question)
  1. If x, y, z be three consecutive intergers, then prove that log(1+xz) =...

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  2. If 1 + log(10)a = 2log(10)b, then express a in terms of b^2.

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  3. If 3+log(10)x = 2log(10)y, then express x in terms of y.

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  4. Calculate : (i) (logsqrt(27)+log8-logsqrt(1000))/(log 1.2)

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  5. Calculate : log(3)4 xx log(4)5 xx log(5)6 xx log(6)7 xx log(7)3

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  6. Calculate : (iii) log10(384/5)+log(10)(81/32)+3log(10)(5/3)+log(10)(...

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  7. Calculate : log(x^2)x xx log(y^2)y xx log(z^2)z

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  8. Prove that (ii) log(10)15(1+log(15)30)+1/2 log(10)16(1+log(4)7)-log(...

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  9. Prove that log(2)log(2)log(4)256+2log(sqrt2)2=5

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  10. Prove that log(b^3)a xx log(c^3)b xx log(a^3)c = 1/27

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  11. Prove that (v) 1/(log(xy)(xyz)) + 1/(log(yz)(xyz)) + 1/(log(zx)(xyz)...

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  12. Prove that (vi) log((a^2)/(bc)) + log ((b^2)/(ca)) + log ((c^2)/(ab)...

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  13. Prove that x^(log y - logz) xx y^(log z - logx) xx z^(log x - log y)...

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  14. Prove that log(7)sqrt(7sqrt(7sqrt(7....................oo))) = 1

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  15. If log((x+y)/5) = 1/2 (log x + log y), then show that x/y + y/x = 23.

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  16. If a^(4) + b^(4) = 14 a^(2)b^(2), then show that log(a^(2) + b^(2)) = ...

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  17. If (log x)/(y-z) = (log y)/(z-x) = (log z)/(x-y), then prove that xyz ...

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  18. If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b), then prove that x...

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  19. If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b), then prove that x^...

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  20. If a^(3-x).b^(5x) = a^(5+x).b^(3x), then show that x log (b/a) = log a...

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