Question

a=2x^-1/2x^-2,b=2^-x/2^x-11 and a-b=0 find the value of x​

Answer 1

Explanation:

a = 2^(x-1) / 2^(x-2) = 2^ ( x-1 -x +2) = 2^1 = 2

Now with b

b = 2^(-x) / 2^(x+1) = 2^(-x -x -1) = 2^(-2x-1)

Given a - b = 0

So 2 - 2^(-2x-1) = 0

Or 2^1 = 2^(-2x-1)

Equating power of same base 2, we have - 2x - 1 = 1

Or - 2x = 2

So x = -1