Question

Solve for x.
2^4x-1/2^3x+2=4

Answer 1

let z = 2^x, and you have

z^4 - 1/z^2 + 2 = 4
(z^6 - 1)/z^2 = 2

don't like that. How about

(z^4 - 1)/(z^3 + 2) = 4
z^4 - 1 = 4z^3 + 8
z^4 - 4z^3 - 9 = 0

still no joy. You sure there's no typo somewhere?

Ah. how about

2^(4x-1) / 2^(3x+2) = 4
since we're dividing, subtract exponents to get

2^(x-3) = 4

now, 4 = 2^2, so we have

2^(x-3) = 2^2
x-3 = 2
x = 5

See how important parentheses can be?

Answer 2

Thank you.