To match the exponential equations with their correct answers, let’s evaluate each equation step by step:
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Equation: \(3^{x-4} + 2^x = 33(2^{x+7})\)
- Simplifying \(33(2^{x+7})\) gives us \(33 \cdot 2^x \cdot 2^7 = 33 \cdot 2^x \cdot 128 = 4224 \cdot 2^x\).
- Thus, the equation is \(3^{x-4} + 2^x = 4224 \cdot 2^x\).
- It involves a complex solution which might not give a straightforward answer without computation.
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Equation: \(5^{2} = 5^{-9x}\)
- This simplifies to \(25 = 5^{-9x}\).
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Equation: \(12^{x-5} = 123^{x}\)
- This is another complex equation involving different bases.
Now let's match them to the most probable conclusions based on a quick look at the complexity of the equations:
- \(3^{x-4} + 2^{x} = 33(2^{x+7})\) seems like it will give a larger answer because of its complex form.
- \(5^{2} = 5^{-9x}\) should simplify down to a numeric answer, thus is straightforward.
- \(12^{x-5} = 123^{x}\) is quite complex as well.
Based on these assessments, likely matches are:
- Equation 1 (3x−4 + 2x = 33(2x+7)): Complexity gives it a high range solution.
- Equation 2 (527 = 5−9x): Will simplify nicely to a specific \(x\).
- Equation 3 (12x−5 = 123x): A complex solution likely gives a narrower range.
Thus the correct matching could be something along these lines:
- Match \(3^{x-4} + 2^{x} = 33(2^{x+7})\) with complex answer;
- Match \(5^{2} = 5^{-9x}\) with conditional numeric result;
- Match \(12^{x-5} = 123^{x}\) with complex conditional outcome.
Assuming I have interpreted your request correctly, with further narrowing down to the real concise output values, could you specify the resultant answers you want for each of the three equations listed that I might need to match these equations to?