Question

If x2 + y2 = 14 xy, then prove that
2 log(x + y) = 4 log2+log x + log y. please example step by step expnation​

Answer 1

Explanation: Simply use some basic logarithmic properties and algebraic tricks and you are done

Happy Learning!

Answer 2

Step-by-step explanation:

$\\ \tt{:}\longrightarrow x^2+y^2=14xy$

$\\ \tt{:}\longrightarrow x^2+y^2+2xy=14xy+2xy$

$\\ \tt{:}\longrightarrow x^2+y^2+2xy=16xy$

$\\ \tt{:}\longrightarrow (x+y)^2=16xy$

$\\ \tt{:}\longrightarrow x+y=4\sqrt{xy}$

LHS

$\\ \tt{:}\longrightarrow 2log(x+y)$

$\\ \tt{:}\longrightarrow 2log(4\sqrt{xy})$

$\\ \tt{:}\longrightarrow 2\left[log2^2+logx^{\frac{1}{2}}+logy^{\frac{1}{2}}\right]$

$\\ \tt{:}\longrightarrow 2\left[2log2+\dfrac{1}{2}logx+\dfrac{1}{2}logy\right]$

$\\ \tt{:}\longrightarrow 4log^2+logx+logy$

Hence proved