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.