Basic of Logarithms
medium

જો ${\log _e}\left( {{{a + b} \over 2}} \right) = {1 \over 2}({\log _e}a + {\log _e}b)$, તો $a$ અને $b$ વચ્ચેનો સંબંધ મેળવો.

A

$a = b$

B

$a = {b \over 2}$

C

$a =2 b$

D

$a = {b \over 3}$

Solution

(a) ${\log _e}\left( {{{a + b} \over 2}} \right) = {1 \over 2}({\log _e}a + {\log _e}b)$

$ = {1 \over 2}{\log _e}(ab) = {\log _e}\sqrt {ab} $

$ \Rightarrow {{a + b} \over 2} = \sqrt {ab} \,\, \Rightarrow a + b = 2\sqrt {ab} $

==> $\,a = b$.

Standard 11
Mathematics

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