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The value of (log(10)2)^3+log(10)8log(10...

The value of `(log_(10)2)^3+log_(10)8log_(10)5+(log_(10)5)^3` is ............

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The correct Answer is:
1
Let ` log_(10)2 = p and log_(10) 5 = q`
Hence, p+q = 1
` x = p^(3) + 3pq + q^(3)`
` = (p+q)^(3) - 3 pq(p+q)+3 pq`
` = 1-3pq+3pq`
= 1
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CENGAGE-LOGARITHM AND ITS PROPERTIES-Exercise (Numerical)
  1. If log(a)b=2, log(b)c=2, and log(3) c= 3 + log(3) a,then the value of...

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  2. The value of (log(10)2)^3+log(10)8log(10)5+(log(10)5)^3 is ..............

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  3. If (log)4A=(log)6B=(log)9(A+B),t h e n [4(B/A] (where [ ] represents t...

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  4. Integral value of x which satisfies the equation =log6 54+(log)x 16=(l...

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  5. If a = log(245) 175 and b = log(1715) 875, then the value of (1-ab)/...

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  6. The difference of roots of the equation ((log)(27)x^3)^2=(log)(27)x^6 ...

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  7. Sum of all integral values of x satisfying the inequality (3^((5/2)log...

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  8. The least integer greater than (log)2 15 (log)(1/6)2(log)3 1/6 is .......

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  9. The reciprocal of 2/((log)4(2000)^6)+3/((log)5(2000)^6) is ..............

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  10. Sum of integers satisfying sqrt((log)2x-1)-1/2(log)2(x^3)+2>0 is......

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  11. Number of integers satisfying the inequality (log)(1/2)|x-3|>-1 is.......

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  12. Number of integers lt=10 satisfying the inequality 2(log)(1/2)(x-1)lt=...

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  13. The value of (sqrt(3+2sqrt2)+sqrt(3-2sqrt2))^(2^(9)) is .

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  14. The value of 5^((log)(1/5)(1/2))+(log)(sqrt(2))4/(sqrt(7)+sqrt(3))+(lo...

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  15. The value of N=((log)5 250)/((log)(50)5)-((log)5 10)/((log)(1250)5) is...

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  16. if x+log10 (1+2^x)=xlog10 5+log10 6 then x

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  17. The x , y , z are positive real numbers such that (log)(2x)z=3,(log)(5...

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  18. If a=(log)(12)18 , b=(log)(24)54 , then find the value of a b+5(a-b)do...

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