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Question: Answered & Verified by Expert
The function $L(x)=\int_1^x \frac{d t}{t}$ satisfies the equation
MathematicsDefinite IntegrationJEE Main
Options:
  • A $L(x+y)=L(x)+L(y)$
  • B $L\left(\frac{x}{y}\right)=L(x)+L(y)$
  • C $L(x y)=L(x)+L(y)$
  • D None of these
Solution:
1089 Upvotes Verified Answer
The correct answer is: $L(x y)=L(x)+L(y)$
Given function $L(x)-\int_1^x \frac{1}{t} d t=[\log t]_1^x=\log x-\log 1$
$\Rightarrow L(x)-\log x$, Hence $L(x y)=L(x)+L(y)$.

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