C-1 4^x-2^(x+3)+12=0 [2;3]

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To solve the equation (4^x - 2^{x+3} + 12 = 0) on the interval ([2, 3]), we can use a graphical approach or the intermediate value theorem as it's difficult to solve algebraically.

Here is how you can solve it using a graphical approach:

Upon graphing the function, you will see that there is a solution on the interval ([2, 3]) where the graph intersects the x-axis.

If you're looking for an algebraic way to solve this equation with the given interval, we can rewrite the equation as:

[4^x - 2^{x+3} + 12 = 0]

Substitute (2^{x+3}) with (2^x \times 2^3 = 8 \times 2^x):

[4^x - 8 \times 2^x + 12 = 0]

Factor out (2^x):

[2^x (2^x - 8) + 12 = 0]

[2^x (2^x - 8) = -12]

Unfortunately, it is challenging to solve this algebraically within the given interval, so using a graphical method or numerical methods, such as Newton's method, may be more practical for finding the solution.