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Integration of Piecewise Continuous Functions

log 6 = 2 log...

Question

log 6 = 2 log 5 + log 4 - log 3 - log 2

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Solution

$l o g 6 + 2 l o g 5 + l o g 4 - l o g 3 - l o g 2$
$= l o g 6 + 2 l o g 5 + {l o g 2}^{2} - (l o g 3 + l o g 2)$
$= l o g 6 + 2 l o g 5 + 2 l o g 2 - l o g (3 \times 2)$
$= l o g 6 + 2 (l o g 5 + l o g 2) - l o g 6$
$= l o g 6 + 2 l o g (5 \times 2) - l o g 6$
$= 2 l o g 10$
$= 2$
(In the portal, the question has been wrongly printed as $l o g 6 = 2 l o g 5 + l o g 4 - l o g 3 - l o g 2$ )

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Log6+ 2log5+log4-log3-log2=2

Prove it

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