The given equation is:

\[
3^{x2} - 4x = \frac{1}{27}.
\]

Let's clarify and rewrite it step by step. If this equation represents \( 3^{x \cdot 2} - 4x = \frac{1}{27} \), the solution will differ from \( 3^{x2 - 4x} = \frac{1}{27} \).

Let me know if you meant:
1. \( 3^{x \cdot 2 - 4x} = \frac{1}{27} \),
2. \( 3^{x2 - 4x} = \frac{1}{27} \),
3. \( 3^{x2} - 4x = \frac{1}{27} \), or
4. \( (3^x)(2) - 4x = \frac{1}{27} \).

Please clarify so I can proceed!

Discover how to solve the exponential equation 3^(x2 - 4x) = 1/27 with step-by-step guidance. This problem explores concepts in algebra and exponents, including the properties of exponents and equality of exponential equations. Ideal for high school students in Grades 9-12.

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