Question

prove that log 75/16-2 log 5/9 +log 32/243 = log2​

Answer 1

Step-by-step explanation:

Dimensions of a rectangular plot:

$Let \: Length = l \: m \: and \: breadth = b \: m$

$i) Perimeter \: of \: the \: plot = 36 \: m$

$\implies 2( l + b ) = 36$

$\implies l + b = \frac{36}{2}$

$\implies b = 18 - l \: --(1)$

$ii ) Area \: of\: the \: plot = l \times b \: --(2)$

/* According to the problem given */

$If \: the \: length \: is \: increased \: by \: 6\:m\\and \: the \: breadth \: is \: decreased \: by \\ 3\:m\: then$

New Dimensions of the rectangular plot:

$Length = ( l + 6 )\: m \: and \\breadth = ( b - 3 ) \: m$

$Area \: of \: the \: new \: plot = ( l+6)(b-3) \:--(3)$

$\pink{ (l+6)(b-3) = l \times b }$

$\implies l( b-3) + 6( b -3 ) = lb$

$\implies \cancel {lb} - 3l + 6b - 18 =\cancel { lb}$

$\implies -3l + 6b - 18 = 0$

/* Dividing each term by 3 , we get */

$\implies - l + 2b - 6 = 0$

$\implies - l + 2( 18 - l ) = 6\: [ From \: ( 1 ) ]$

$\implies - l + 36 - 2l = 6$

$\implies - 3l = 6 - 36$

$\implies -3l = -30$

$\implies l = \frac{ -30}{-3}$

$\implies l = 10$

Therefore.,

$\red{ Length \: of \: the \: plot } \green { = 10\:m }$

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