2^2x-1+2^2x-2+2^2x-3<448

To simplify the expression, let's rewrite it as follows: 2^(2x-1) + 2^(2x-2) + 2^(2x-3) < 448 Now, we can rewrite the powers of 2 to make the expression easier to work with: 2^(2x-1) = 2^2 * 2^(2x-3) = 4 * 2^(2x-3) 2^(2x-2) = 2^1 * 2^(2x-3) = 2 * 2^(2x-3) 2^(2x-3) = 2^(2x-3) By substituting these back into the original expression, we get: 4 * 2^(2x-3) + 2 * 2^(2x-3) + 2^(2x-3) < 448 Now, factor out 2^(2x - 3): (4 + 2 + 1) * 2^(2x-3) < 448 7 * 2^(2x-3) < 448 Now, divide both sides by 7: 2^(2x-3) < 64 Since 64 can be written as 2^6, we can rewrite the inequality as: 2^(2x-3) < 2^6 Now, since the bases are the same, we can compare the exponents: 2x - 3 < 6 Adding 3 to both sides: 2x < 9 Dividing by 2: x < 4.5 Therefore, the solution to the inequality is x < 4.5.