[tex]\begin{aligned} \sf {81}^{5x + 3} &= \sf {27}^{6x - 4} \\ \sf {( {3}^{4}) }^{5x + 3}&= \sf {( {3}^{3} )}^{6x - 4} \\ \sf {3}^{20x + 12} &= \sf {3}^{18x - 12} \\ \sf 20x + 12 &= \sf 18x - 12 \\ \sf 20x - 18x&= \sf - 12 - 12 \\ \sf 2x&= \sf - 24 \\ \sf x &= \sf \frac{ - 24}{2} \\ \sf x &= \sf - 12 \end{aligned}[/tex]
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[tex]\begin{aligned} \sf {81}^{5x + 3} &= \sf {27}^{6x - 4} \\ \sf {( {3}^{4}) }^{5x + 3}&= \sf {( {3}^{3} )}^{6x - 4} \\ \sf {3}^{20x + 12} &= \sf {3}^{18x - 12} \\ \sf 20x + 12 &= \sf 18x - 12 \\ \sf 20x - 18x&= \sf - 12 - 12 \\ \sf 2x&= \sf - 24 \\ \sf x &= \sf \frac{ - 24}{2} \\ \sf x &= \sf - 12 \end{aligned}[/tex]