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Prove that log(a^(2)/(bc))+log(b^(2)/...

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

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

Show that a^(log_(a^2)^(x))xxb^(log_(b^2)^(y))xxc^(log_(c^2)^(z))=sqrt(xyz)

If log(a+b+c) = log a + log b + log c , then prove that log ((2a)/(1-a^(2))+(2b)/(1-b^(2))+(2c)/(1-c^(2))) = log(2a)/(1-a^(2)) + log (2b)/(1-b^(2)) + log(2c)/(1-c^(2)) .

If f(x)=((a+x)/(b+x))^(a+b+2x) , prove that, f'(0) =[2"log"(a)/(b) +(b^(2)-a^(2))/(ab)]((a)/(b))^(a+b) .

Prove that : (iv) a^(log_(a^2)x) xx b^(log_(b^2)y) xx c^(log_(c^2)z) = sqrt(xyz)

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

If a+b+c =0 Prove that root(bc)(x^(a^(2))/x^(bc))xxroot(ca)(x^(b^(2))/x^(ca))xxroot(ab)(x^(c^(2))/x^(ab))=1

Prove that : (vi) log_(a)x + log_(a^2)x^(2) + log_(a^3)x^(3) + ………….+ log_(a^n)x^(n) = log_(a)x^(n)

Show that (1)/(log_(a)bc+1)+(1)/(log_(b)ca+1)+(1)/(log_(c )ab+1)=1

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) .

CHHAYA PUBLICATION-LOGARITHM -Short Answer Type Question
  1. Prove that log(75/16)-2log(5/9)+log(32/243)=log2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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