Solve for x.

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?

Thank you.

To solve for x in the equation 2^(4x-1) / 2^(3x+2) = 4, we can start by simplifying the equation.

First, let's simplify the expression on the left-hand side of the equation by using the rules of exponents. According to the rule that states a^(m-n) = a^m / a^n, we know that 2^(4x-1) / 2^(3x+2) is equal to 2^(4x-1 - (3x+2)), which simplifies to 2^(4x-3x-3).

Now, we can rewrite the equation as 2^(4x-3x-3) = 4.

Next, let's express both sides of the equation with the same base of 2. Since 4 can be expressed as 2^2, the equation becomes 2^(4x-3x-3) = 2^2.

According to the rule of exponents that states if a^m = a^n, then m = n, we know that 4x - 3x - 3 = 2.

Now, let's solve for x. Combine like terms: x - 3 = 2.

Adding 3 to both sides of the equation, we find that x = 5.

Therefore, the solution to the equation 2^(4x-1) / 2^(3x+2) = 4 is x = 5.