Question

if a is not equals to plus minus b and a + b is not equal to 1 then find the value of x satisfying the equation (a^4-2a^2b^2+b^4)^x-1 = (a-b)^2x(a+b)^-2

Answer 1

Here it is !!
Hope u like it

Answer 2

Final Answer :
$log( \frac{a - b}{a + b} )$
Steps:
1)
$( { {a}^{4} - 2 {a}^{2} {b}^{2} + {b}^{4} ) }^{x - 1} = \: {(a - b)}^{2x} {(a + b) }^{ - 2} \\ = > {( {a}^{2} - {b}^{2} ) }^{2x - 2} = {(a - b)}^{2x} ( {a + b)}^{ - 2} \\ = > {(a + b)}^{2x - 2} {(a - b)}^{2x - 2} = {(a - b)}^{2x} {(a + b)}^{ - 2} \\ = > {(a + b)}^{2x} = {(a - b)}^{2} \\ taking \: log \: \\ = > 2x log(a + b) = 2 log(a - b) \\ = > x = \frac{ log(a - b) }{ log(a + b) }$

2 ) In last fourth step, we cancelled some terms,
as a! =±b and a+b !=1