To solve the equation \( 27^{\frac{3}{4} - 1} = 26 \), we first simplify the left side.
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Start with the exponent: \( \frac{3}{4} - 1 = \frac{3}{4} - \frac{4}{4} = \frac{3 - 4}{4} = \frac{-1}{4} \).
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Rewrite the equation: \[ 27^{\frac{-1}{4}} = 26 \]
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Rewrite \( 27 \) as \( 3^3 \): \[ (3^3)^{-\frac{1}{4}} = 26 \] \[ 3^{-\frac{3}{4}} = 26 \]
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Take the reciprocal: \[ \frac{1}{3^{\frac{3}{4}}} = 26 \]
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Inverting gives: \[ 3^{\frac{3}{4}} = \frac{1}{26} \]
Now, we need to analyze the options given:
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\( \frac{25}{27} \)
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\( 1 \)
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\( 0 \)
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\( 3 \)
Since \( 3^{\frac{3}{4}} \) is not 1, 0, or 3, we'll calculate the approximate value of \( 3^{\frac{3}{4}} \).
Taking \( 3^{0.75} \) directly: \[ 3^{0.75} \approx 2.279 \]
Thus, it's not equal to any of the provided options, but since none of these directly solve for \( x \) in the form given, we might need to consider:
- Rearranging back or reevaluating if it's an arbitrary check based on number sense — yet \( 26 \) is significantly larger than any of these choices besides the \( 1 \).
However, resolving the exact interpretation and calculation seems neglected here under exponent rules, nevertheless with a numerical evaluation \( 3^{\frac{3}{4}} \) appears closer akin to approximating if ratio-led insight into each divisor indicative of fraction checks.
Since the problem's restrictions suggest a calculative output or raw distance from integers; the nearest viable option gauged around an equal point shaping might thus land at:
Thus, the correct answer could be \( 1 \) if seeking measurable proximity within groupings, but needs review if those foundational checks exist beyond mere ratio-based notation interchangeably.
Conclusion:
Among the provided options without numerical precision guiding directly to ratio, choose \( 1 \).