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If ((log)a N)/((log)c N)=((log)a N-(log)...

If `((log)_a N)/((log)_c N)=((log)_a N-(log)_b N)/((log)_b N-(log)_c N),w h e r eN >0a n dN!=1, a , b , c >0` and not equal to 1, then prove that `b^2=a c`

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ALLEN-LOGARITHMS-All Questions
  1. A rational number which is 50 times its own logarithm to the base 10 ...

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  2. 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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  3. 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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  4. 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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  5. Prove that (log)7 10 is greater than (log)(11)13.

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

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

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

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

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

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  12. Solve : log(3//4)log(8)(x^(2)+7)+log(1//2)log(1//4)(x^(2)+7)^(-1)=-2.

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  13. Given: (log)(10)34. 56=1. 5386 find (log)(10)3. 456 and(log)(10)0....

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

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

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

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

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  18. Find the value of x satisfying the equation ((log)3 root(3)(3x)+(log)x...

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  19. The number of solutions of (log)4(x-1)=(log)2(x-3) is (a) 3 (b) 1 (...

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  20. Let (x0, y0) be the solution of the following equations: (2x)^(1n2)=(3...

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