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Prove that log(b^(3))axxlog(c^(3))bxx...

Prove that
`log_(b^(3))axxlog_(c^(3))bxxlog_(a^(3))c=1/27`

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Prove that log_(b^3)a xx log_(c^3)b xx log_(a^3)c = 1/27

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If a > 0, c > 0, b = sqrt(ac), ac != 1 and N > 0 , then prove that (log_(a)N)/(log_(c )N) = (log_(a)N - log_(b)N)/(log_(b)N - log_(c )N) .

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If a,b,c are in A.P and x,y,z are in G.P then prove that a^((b-c)log_(a)^(x))xxb^((c-a)log_(b)^(y))xxc^((a-b)log_(c )^(z))=1

Prove that 1/3<(log)_(10)3<1/2dot

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Find the values : log_(2)[log_(2){log_(3)(log_(3)27^(3))}]

CHHAYA PUBLICATION-LOGARITHM -Short Answer Type Question
  1. Prove that log(2)log(2)log(4)256+2log(sqrt2)2=5

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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