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Prove that a^x-b^y=0\ w h e r e\ x="\ "s...

Prove that `a^x-b^y=0\ w h e r e\ x="\ "sqrt(("log")_a b)\ &\ y=sqrt((log)_b a\ ),\ a >0,\ b >0\ &\ a ,\ b!=1`

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ALLEN-LOGARITHMS-All Questions
  1. If x=1+(log)a b c ,\ y=1+(log)b c a\ a n d\ z=1+(log)c a b ,\ then pr...

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  2. A rational number which is 50 times its own logarithm to the base 10, ...

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  3. Prove that a^x-b^y=0\ w h e r e\ x="\ "sqrt(("log")a b)\ &\ y=sqrt((lo...

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  4. If ((log)a N)/((log)c N)=((log)a N-(log)b N)/((log)b N-(log)c N),w h e...

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  5. If (log)b a(log)c a+(log)a b(log)c b+(log)a c(log)bc=3 (where a , b ,...

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  6. Prove that (log)7 10 is greater than (log)(11)13.

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  7. Solve the system the equations (a x)^(loga)=(b y)^(logb); b^(logx)=a^(...

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  8. Solve for x :(log)5 120+(x-3)-2.(log)5(1-5^(x-3))=-(log)5(0. 2-5^(x-4)...

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  9. Solve the equation for x : log4+(1+1/(2x))log3=log(root(x)3+27)

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  10. Find the real solutions to the system of equations log(10)(2000xy)-log...

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  11. Find the x satisfying the equation log^2(1+4/x)+log^2(1-4/(x+4))=2lo...

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  12. Solve for x:\ log^2 (4-x)+log(4-x)*log(x+1/2)-2log^2(x+1/2)=0

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  13. Solve the following equation for x\ &\ y :(log)(100)|x+y|=1/2,(log)(10...

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  14. Find all real numbers x which satisfy the equation 2(log)2log\ 2x+(...

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  15. log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2+7)^(-1)=-2

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  16. Given: (log)(10)34. 56=1. 5386\ fin d(log)(10)3. 456 :(log)(10)0. 0...

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  17. Find the number of positive integers which have the characterstics 3 w...

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  18. If (log)(10)2=0. 3010\ &(log)(10)3=0. 4771.\ Find the value of (log...

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  19. Find the antilogarihtm of 0.75 if the base of the logarithm is2401

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  20. Let 'L' denotes the antilog of 0.4 to the base 1024. and 'M' denotes t...

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