To solve the exponential equations given, we will work through them step by step.
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For the first equation:
\( 12^{2-5} = 12^{x} \)
Simplifying the left side:
\( 12^{-3} = 12^{x} \)
Therefore, \( x = -3 \). -
For the second equation:
\( 3^{x-4} + 2^{x} = 1.23^{x} \) (Assuming a format correction as the equation isn't clearly defined). Solving this would typically require a numerical method or graphing, and cannot be directly solved without further context. -
For the third equation:
\( 3^{3}(2^{x+7}) = 5^{2} \)
Equals \( 27 \cdot 2^{x+7} = 25 \).
To isolate \( x \), we find:
\( 2^{x+7} = \frac{25}{27} \)
Solving for \( x \), we would take logarithms for the \( 2^{x} \) term which is again not directly solvable without further specifics. -
The last part states \( 5275 - 93 = 25 \), which appears to be an arithmetic operation and not an exponential equation. The current resolution can be implied as \( x = 3 \).
Final match summary:
- The equation that solved to \( x = -3 \) is matched with \( 12^{2-5} \).
- The equation \( x = 3 \) appears to match the last operation of addition since it's not exponential.
It would be best if you provide clearer formatting for each equation for precise matching and solution steps.
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