Question

If x 2+y2=18xy then prove that 2log(x-y) =4log2+logx+log y

Answer 1

Answer:

If x 2+y2=18xy then prove that 2log(x-y) =4log2+logx+log y

Explanation:

Answer 2

Correct Question :

If x² + y² = 18xy then prove that ,

$\rm \: 2 log(x - y) = 4 log(2 )+ log(x) + log(y)$

Given :

• x² + y² = 18xy

To Prove :

• $\rm \: 2 log(x - y) = 4 log(2) + log(x) + log(y)$

Solution :

Let ,

• x² + y² = 18xy$\longriggtarrow$eq(1)

We have ,

• $\rm \: 2 log(x - y) = 4 log2 + logx + logy$

Consiser the LHS part ,

$\rm \: 2 log(x - y) \\ \\ {\boxed{ \rm{ log(a {}^{m}) = m log(a) }}} \\ \\ : \implies \rm 2 log(x - y) = log {(x - y)}^{2} \\ \\ \boxed {\rm{ (a - b) {}^{2} = {a}^{2} + {b}^{2} - 2ab }} \\ \\ : \implies \rm \: log( {x}^{2} + {y}^{2} - 2xy )$

From eq(1) ,

$: \implies \rm log(18xy - 2xy) \\ \\ : \implies \rm \: log(16xy) \\ \\ \boxed {\rm{ log(ab) = log(a) + log(b) }} \\ \\ : \implies \rm \: log(16) + log(x) + log(y) \\ \\ : \implies \rm log( {2}^{4} ) + log(x) + log(y) \\ \\ : \implies \rm \: 4 log(2) + log(x) + log(y) \\ \\ : \implies \rm \: RHS$

⠀⠀⠀⠀⠀⠀⠀⠀HENCE PROVED