Let f(x) a^ x-1 b^ x-1 and g(x)=x-1 . What is _ x 1 f(x)^ 1 g(x) equal to?

Step-by-step solution

Since, aligned & Since, _ x 1 f(x) 1 g(x) & = _ x 1 ( a^ x-1 +b^ x-1 2 )^ 1 x-1 aligned (it is form 1^ ) aligned & = e ^ _ x 1 ( a ^ a -1 + b ^ x -1 2 -1 ) 1 x -1 = e ^ _ x ~m ( a ^ x -1 -1 2( x -1) + b ^ x -1 -1 2( x -1) ) & =e^ ( 1 2 a+ 1 2 mb b ) =e^ 1 2 (a b) = a b aligned