Mathematics: Given that (2*(x -3) ) / 8*( 2 y - 3) = 16*( x - y )

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Given that (2*(x -3) ) / 8*( 2 y - 3) = 16*( - id238231613961107, gabbytopper8373

Ответ:

razerocfu4523

18.08.2021

Mathematics

Step-by-step explanation:

$\frac{2^{x-3}}{8^{2y-3}}=16^{x-y}\\\\\frac{2^{x-3}}{(2^{3})^{2y-3}}=(2^{4})^{x-y}\\\\\frac{2^{x-3}}{2^{3*(2y-3)}}=2^{4*(x-y)}\\\\\frac{2^{x-3}}{2^{6y-9}}=2^{4x-4y}\\\\2^{x-3 -(6y-9)}=2^{4x-4y}\\\\2^{x-3-6y+9}=2^{4x-4y}\\\\2^{x-6y+6}=2^{4x-4y}$

base is same, so equate the powers

x - 6y + 6 = 4x - 4y

Subtract 'x' from both sides

-6y + 6 = 4x -x - 4y

-6y + 6 = 3x - 4y

Add '6y' to both sides

6 = 3x - 4y + 6y

6 = 3x + 2y

Hence proved

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Given that (2(x -3) ) / 8( 2 y - 3) = 16*( x - y )

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Given that (2(x -3) ) / 8( 2 y - 3) = 16*( x - y )