exponential equation a question with the phrase "in terms of"

Question

3-2^x=a

3-2^{-x =b}

find a in terms of b

can anyone solve that question step by step, please? thanks a lot.

Answer 1

3 - 2^x = a, so 2^x = 3-a

 

3 - 2^-x = b, so 2^-x = 3 - b, which is equivalent to 2^x = 1/(3 - b)

 

Therefore, 3 - a = 1/(3 - b)

 

(3 - a)(3 - b) = 1

 

9 -3a - 3b + ab = 1

 

ab - 3a = 3b - 8

 

a(b - 3) = 3b - 8

 

a = (3b - 8)/(b - 3)