Select the correct answer to the following equation: 27x3/4−1=26

To solve the equation \( 27^{\frac{3}{4} - 1} = 26 \), we first simplify the left side.

1. Start with the exponent:
\( \frac{3}{4} - 1 = \frac{3}{4} - \frac{4}{4} = \frac{3 - 4}{4} = \frac{-1}{4} \).

2. Rewrite the equation:
\[
27^{\frac{-1}{4}} = 26
\]

3. Rewrite \( 27 \) as \( 3^3 \):
\[
(3^3)^{-\frac{1}{4}} = 26
\]
\[
3^{-\frac{3}{4}} = 26
\]

4. Take the reciprocal:
\[
\frac{1}{3^{\frac{3}{4}}} = 26
\]

5. Inverting gives:
\[
3^{\frac{3}{4}} = \frac{1}{26}
\]

Now, we need to analyze the options given:

1. \( \frac{25}{27} \)

2. \( 1 \)

3. \( 0 \)

4. \( 3 \)

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** \( 1 \).