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If log(a)b +log(b)c = +log(c) a vanishes...

If `log_(a)b +log_(b)c = +log_(c)` a vanishes where a,b and c are positive reals different than unity then the value of `(log_(a)b)^(3)+(log_(b)c)^(3) +(log_(c)a)^(3)` is

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ALLEN -LOGARITHMS-All Questions
  1. If a^2+b^2=23 a b , then prove that log((a+b))/5=1/2(loga+logb)dot

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  2. If (log)kx . (log)5k=(log)x5,k!=1,k >0, then x is equal to k (a) k ...

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  3. If log(a)b +log(b)c = +log(c) a vanishes where a,b and c are positive ...

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  4. Evaluate : 3(40)^(1/3)-4 (320)^(1/3)-(5)^(1/3)

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  5. If ||x-1|-2|=5 then find x

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  6. If |x-1|+|x+1|=2, then find x.

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  7. Solve the equation |x-1|+|7-x|+2|x-2|=4

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  8. Prove that sqrt (7) is an irrational number.

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  9. If in a right angled triangle, a\ a n d\ b are the lengths of sides ...

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  10. Solve : (log)((2"x"-1))\ ((x^4+2)/(2x+1))\ =1

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  11. 1/((log)(sqrt(b c))a b c)+1/((log)(sqrt(c a))a b c)+1/((log)(sqrt(a b)...

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  12. The ratio (2^(log(2)a^4)-3^(log(27)(a^2+1)^3)-2a)/((7^(4log(49)a)-a-1)...

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  13. The value of expression, (log)4((x^2)/4)-2(log)4(4x^4) when x=-2 is ...

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  14. If 1/a+1/b+1/c = 1/(a+b+c) then (a+b)(b+c)(c+a)=....... a.a b c ...

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  15. Which one of the following denotes the greatest positive proper frac...

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  16. If p=s/((1+k)^n),\ t h e n\ n\ equals a.logs/(p(1+k)) b. (log(s/p)...

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  17. Value of x satifying (log)(10)sqrt(1+x)+3(log)(10)sqrt(1-x)=(log)(10)s...

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  18. Given system of simultaneous equations 2^x\ . 5^y=1\ a n d\ 5^(x+1). 2...

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  19. The value of N satisfying (log)a[1+(log)b\ {1+(log)c(1+(log)p N)}]=0 i...

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  20. If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 ...

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