Question

if (a/b)^x-1=(b/a)^x-3 , find the value of 'x'. (assume a is not equal to b)​

Answer 1

210

Step-by-step explanation:

f(g(x))=a(bx+a)+b

=abx+a^2+b

g(f(x))=b(ax+b)+a

Therefore f(g(x))−g(f(x))

=abx+a^2+b−(abx+b^2+a)

=a^2−b^2+b−a

=(a−b)(a+b−1)

Since it is a constant function

(a−b)(a+b−1)=28

(a−b)(a+b−1)=4(7)

Hence a−b=4

a+b=8

a=6 and b=2

Hence ab=12

Also

(a−b)(a+b−1)=(1)(28)

a−b=1

a+b=29

a=15 and b=14

Therefore ab=14(15)=210