Answer:
m = n-1
Step-by-step explanation:
2^m + 2^m = 2^n
Add on the left
2( 2^m) = 2 ^ n
2^1 ( 2^m) = 2^n
We know that a^b* a^c = a^ (b+c)
2^(1+m) = 2^n
The bases are the same so the exponents are the same
1+m = n
Solving for m
1+m-1 = n-1
m = n-1
Given :
2^m + 2^m = 2ⁿ
→ 2(2^m) = 2ⁿ
→ 2¹ × 2^m = 2ⁿ
→ 2^(1 + m) = 2ⁿ
As bases are equal, exponents are equal too.
→ 1 + m = n
→ m = n - 1
