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If x=1+(log)a b c ,\ y=1+(log)b c a\ a n...

If `x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ ` then prove that `x y z=x y+y z+z xdot`

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ALLEN-LOGARITHMS-All Questions
  1. If x ,\ y >0,(log)y x+(log)x y=(10)/3\ a n d\ x y=144 ,\ t h e n(x+y...

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  2. let y=sqrt(log2(3)log2(12)log2(48)log2(192)+16)-log2(12)log2(48)+10fin...

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  3. 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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  4. A rational number which is 50 times its own logarithm to the base 10 ...

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  5. The value of a^(sqrt((log)a b))-b^(sqrt((log)b a))(w h e r ea ,b >0a n...

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  6. 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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  7. If (log)b a(log)c a+(log)a b(log)c b+(log)a c(log)cc=3 (where a , b , ...

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

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

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  11. The sytem of equations log10(2000xy)-log10x.log10y=4 log10(2yz)-log...

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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. Solve : log(3//4)log(8)(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 find (log)(10)3. 456 and(log)(10)0....

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

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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. Find the production of the positive roots of the equation sqrt2000(x)^...

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