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Prove that x^(log y-logz)xxy^(logz-lo...

Prove that
`x^(log y-logz)xxy^(logz-logx)xxz^(logx-logy)=1`

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CHHAYA PUBLICATION-LOGARITHM -Short Answer Type Question
  1. Prove that log(36/25)^(3)+3log(2/9)-log2=2log(16/125)

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  2. Prove that log(75/16)-2log(5/9)+log(32/243)=log2

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  3. Prove that x^(log y-logz)xxy^(logz-logx)xxz^(logx-logy)=1

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  4. Prove that log(a^(2)/(bc))+log(b^(2)/(ca))+log(c^(2)/(ab))=0

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

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

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  7. Prove that log(b^(3))axxlog(c^(3))bxxlog(a^(3))c=1/27

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  8. Prove that log a+log a^(2)+loga^(3)+….+loga^(n)=(n(n+1))/(2)loga

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  9. Prove that log a+log a^(3)+loga^(5)+….+loga^(2n-1)=n^(2) loga

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  10. Prove that log(1/y)x xx log(1/z)yxx log(1/x)z=-1

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  11. Prove that log(x^(2))x xx log(y^(2))yxx log(z^(2))=1/8

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  12. Given log(10)2=0.30103 , log(10)e=0.43429, find the value of log(e )(...

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  13. If a^(2)+b^(2)=7ab show that log[1/3(a+b)]=1/2(log a+logb)

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  14. If log((x+y)/(5))=1/2(logx+logy)show that x/(y)+(y)/(x)=23

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

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

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

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  18. If (logx)/(b-c)=(logy)/(c-a)=(logz)/(a-b) prove that (a) x^(a)y^(b)z...

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  19. If a sequence of posivtive numbers are in G.P show that their logar...

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  20. The first and the last terms of a G.P are a and k respectively if the...

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