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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 PUBLICATION-LOGARITHM AND ITS PROPERTIES-Numerical Value Type
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