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To simplify the equation \( 3^{n+4}-6=3^{n+1} \), we can rewrite it as \( 3^{n+4} - 3^{n+1} = 6 \). Factoring out \( 3^{n+1} \) gives us \( 3^{n+1}(3^3 - 1) = 6 \). This simplifies to \( 3^{n+1}(27 - 1) = 6 \) or \( 3^{n+1} \cdot 26 = 6 \). From here, we can isolate \( 3^{n+1} \) as \( 3^{n+1} = \frac{6}{26} = \frac{3}{13} \). Finally, taking logarithms can help us solve for \( n \). In a nutshell, that’s how you simplify the expression while keeping things fun with a little algebraic flair!