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Prove that : (v) p^(log(x)q) = q^(log(...

Prove that :
(v) `p^(log_(x)q) = q^(log_(x)p)`

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CALCUTTA BOOK HOUSE-LOGARITHM-Exercise - 7 (Long-answer type questions)
  1. Prove that : (iii) (yz)^(log(y/z))(zx)^(log(z/x))(xy)^(log(x/y)) = 1

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  2. Prove that : (iv) a^(log(a^2)x) xx b^(log(b^2)y) xx c^(log(c^2)z) = ...

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  3. Prove that : (v) p^(log(x)q) = q^(log(x)p)

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  4. Prove that : (vi) log(a)x + log(a^2)x^(2) + log(a^3)x^(3) + ………….+ l...

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  5. Prove that : (vii) log(sqrt a)b.log(sqrt(b))c.log(sqrt(c ))a = 8.

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

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  7. If x^(2)+y^(2)=z^(2), then prove that 1/(log(z-y)x) + 1/(log(z+y)x) = ...

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  8. If a = log(12)m and b = log(18)m, then prove that log(3)2= (a-2b)/(b-2...

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  9. If x^(2)+y^(2) = 6xy, then prove that 2log(x+y) = log x + logy + 3log2...

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  10. If log((x+y)/2) = 1/3{log x + logy + log(x+y)}, then prove that (x^2)/...

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  11. If a^(2-x).b^(5x) = a^(x+3).b^(3x), then show that x log (b/a) = 1/2 l...

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

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

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  14. If (logx)/(ry-qz) = (log y)/(pz - rx) = (log z)/(qx - py), then prove ...

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  15. If y = a^(1/(1-log(a)x)) and z = a^(1/(1-log(a)y)), then show that x =...

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  16. If x = log(c ) b + log(b)c , y=log(a)c + log(c ) a, z=log(b)a+log(a)b,...

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  17. If a,b,c be three such positive numbers (none of them is 1) that (log(...

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  18. If x = log(2a)a, y = log(3a)2a , z = log(4a)3a, then show that xyz + 1...

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

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  20. If (a(b+c-a))/(loga) = (b(c+a-b))/(logb) = (c(a+b-c))/(logc), then pro...

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