Question:

what do you call "56" in the expression 56 + 2 m​?

Answer:

2^m=2^n+56

or 2^m - 2^n=56

or. 2^n.{2^(m-n) - 1} = 2^0×56 =2^1×28=2^2×14 =2^3×7.

(i). 2^n×{2^(m-n) -1} = 2^0×56.

Comparing the both sides.

n=0. , 2^(m-0) -1=56 or. 2^m=57. => m =log 57 base 2.

(ii). 2^n×{2^(m-n)-1}= 2^1×28.

Comparing the both sides.

n=1. , 2^(m-1). -1 =28 or. 2^(m-1)=29. => m=log 29 base 2. +1 .

(iii). 2^n×{2^(m-n). -1}=2^2×14. ,Comparing

n=2. , 2^(m-2). -1 =14. => m= log 15 base 2. + 2 .

(iv). 2^n×{2^(m-n). -1} = 2^3×7 .

Comparing both sides

n=3. , 2^(m-3). -1 =7 or. 2^(m-3)=2^3 => m-3= 3 or. m =6 .

Thus , m=6 , n=3.