Question

Given 2^m + 2^m = 2^n, express m in terms of n.​

Answer 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

→ m = n - 1 (Answer)

Answer 2

m = n-1

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