Question

if 4 x square + Y square equals to 20 x y then prove that 2 log 2 x -y = 4 log 2 + log x + log y​

Answer 1

hope this helps you☺️

Answer 2

Given: $4x^2+y^2=20xy$

To prove: $2\log(2x-y)=4\log2+\log x+\log y$

Taking left side and to proof right side

$\Rightarrow 2\log(2x-y)$

$\Rightarrow \log(2x-y)^2$                     $\because m\log a=\log a^m$

$\Rightarrow \log(4x^2+y^2-4xy)$                $\because (a-b)^2=a^2+b^2-2ab$

$\Rightarrow \log(20xy-4xy)$                     $\because 4x^2+y^2=20xy$

$\Rightarrow \log(16xy)$                             $\because \log(ab)=\log a+\log b$

$\Rightarrow \log16+\log x+\log y$                $\because 16=2^4$

$\Rightarrow \log2^4+\log x+\log y$                $\because 16=2^4$

$\Rightarrow 4\log2+\log x+\log y$                $\because \log a^m=m\log a$

Hence proved