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Prove that log a+log a^(3)+loga^(5)+…...

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

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CHHAYA PUBLICATION-LOGARITHM -Short Answer Type Question
  1. Prove that log(b^(3))axxlog(c^(3))bxxlog(a^(3))c=1/27

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Prove that : (viii) (log(a)x)/(log(ab)x) = 1+log(a)b.

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  16. If log(p)x=a and log(q)x=b prove that log(p/q)x=(ab)/(a-b)

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  17. If log(x^(2)y^(3))=a and log(x)./(y)=b find log x and logy in terms of...

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  18. If x=(e^(y)-e^(-y))/(e^(y)+e^(-y)) show that y=1/2log(e )((1+x)/(1-x))

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  19. If log(a)b=10 and log(6a)(32b)=5 find the value of a

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  20. If the logarthim of a^(2) top the base b^(3) and the logarithm of b^(...

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