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

MCQ

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

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

✓

Answer

Correct option: C.

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

c
(c) Given function $L(x) = \int_1^x {\frac{1}{t}dt = [\log t]_1^x} $

$= \log x - \log 1$

==> $L(x) = \log x$,

Hence $L\,(xy) = L(x) + L(y)$.

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