The function L(x)= _1^x d t t satisfies the equation - Vidyadip

MCQ

The function $L(x)=\int_1^x \frac{d t}{t}$ satisfies the equation

A
L(x + y) = L(x) + L(y)
B
$L \left(\frac{x}{y}\right)= L (x)+ L (y)$
✓
$L (x y)= L (x)+ L (y)$
D
None of these

✓

Answer

Correct option: C.

$L (x y)= L (x)+ L (y)$

(C)
$L (x)=\int_1^x \frac{1}{ t } dt =[\log t ]_1^x=\log x-\log 1=\log x$
$\therefore \quad L (x y)=\log (x y)=\log x+\log y= L (x)+ L (y)$

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