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Question

The value of 24log(t)tdt is


A

12log(2)2

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B

52log(2)2

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C

32log(2)2

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D

log(2)2

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Solution

The correct option is C

32log(2)2


Explanation for the correct option:

Compute the required value.

Given: 24log(t)tdt

Let,

log(t)=x1tdt=dx

When t=2,x=2

t=log(4),x=log(2)

log(2)log(4)xdx=x22log(2)log(4)log(2)log(4)xdx=12log2(4)-log2(2)log(2)log(4)xdx=12log(4)-log(2)(log(4)+log(2))log(2)log(4)xdx=12log(4×2)log42log(a)-log(b)=logab,log(m)+log(n)=log(mn)log(2)log(4)xdx=12log(8)log2log(2)log(4)xdx=123log(2)log2log(2)log(4)xdx=32log2(2)

Hence, option C is the correct answer.


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