Question

solve this question don't ans if you don't know​

Answer 1

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Answer 2

Solution

Given :-

• [4^(n+1).2^n - 8^n]/ [2^(3m)] = 3/8

To Prove :-

• n + 1 = m

Explanation

Given by question,

➡ [4^(n+1).2^n - 8^n]/ [2^(3m)] = 3/8

➡ [ 2^(2n+2) . 2^n - 2^(3n)]/[2^(3m)} = 3/2^3

➡[ 2^(3n+2) - 2^(3n)]/[2^(3m)] = 3/2^3

➡2^(3n)[(2^2) - 1]/2^(3m) = 3/2^3

➡ 2^(3n-3m) = (3/2^3) × (1/3)

➡ 2^(3n-3m) = 1/2^3

Or,

➡ 2^(3n-3m) = (1/2)^3

Or,

➡2^(3n-3m) = 2^(-3)

We know,

If, a^m = a^n , then,

• m = n,

So,

➡ 3n - 3m = -3

➡ 3n + 3 = 3m

➡3(n+1) = 3m

Or,

➡ n + 1 = m

That's proved.

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