Question

Solve for `x`: `16*4^(x+2) - 16*2^(x+1) + 1 = 0`?

Answer 1

`x=-4`

Explanation:

`16*4^(x+2) - 16*2^(x+1) + 1 =`
`=16^2cdot4^x-2cdot16cdot2^x+1=`
`=16^2cdot(2^x)^2-32cdot 2^x+1=0`

Making `y=2^x`

`16^2y^2-32y+1=0` solving for `y` we have

`y = 1/16=2^x=2^(-4)` then `x=-4`