If a = _ 24 12, ,b = _ 36 24 and c = _ 48 36, then 1+abc is equal… - Vidyadip

MCQ

If $a = {\log _{24}}12,\,b = {\log _{36}}24$ and $c = {\log _{48}}36,$ then $1+abc$ is equal to

A
$2ab$
B
$2ac$
✓
$2bc$
D
$0$

✓

Answer

Correct option: C.

$2bc$

c
(c) $a = {\log _{24}}12 = {{\log 12} \over {\log 24}} = {{2\log 2 + \log 3} \over {3\log 2 + \log 3}}$

$b = {\log _{36}}24 = {{3\log 2 + \log 3} \over {2(\log 2 + \log 3)}}$

$c = {\log _{48}}36 = {{2(\log 2 + \log 3)} \over {4\log 2 + \log 3}}$

$\therefore abc = {{2\,\,\log 2 + \log 3} \over {4\log 2 + \log 3}}$

==> $1 + abc = {{6\log 2 + 2\log 3} \over {4\log 2 + \log 3}} = 2.{{3\log 2 + \log 3} \over {4\log 2 + \log 3}} = 2bc$.

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