Question

Alguém sabe como resolver essa equação exponencial?

Answer 1

$\frac{6^{x-1}+6^{x-2}}{6^{1-x}+6^{2-x}} = 1 \\ \\ ( \frac{6^{x}}{6} + \frac{6^{x}}{6^{2}} ) : (\frac{6}{6^{x}}+\frac{6^{2}}{6^{x}} ) = 1 \\ \\ ( \frac{6^{x}\cdot 6 + 6^{x}}{36} ) : (\frac{6+36}{6^{x}} ) = 1 \\ \\ ( \frac{6^{x}\cdot(6+1)}{36} ) : (\frac{42}{6^{x}} ) = 1 \\ \\ ( \frac{6^{x}\cdot7}{36} ) : (\frac{6\cdot7}{6^{x}} ) = 1 \\ \\ ( \frac{6^{x}\cdot7}{36} ) \cdot (\frac{6^{x}}{6\cdot7} ) = 1 \\ \\ \frac{6^{2x}}{6^{3}}= 1 \\ \\ 6^{2x} = 6^{3} \\ \\ 2x = 3 \\ \\ x = 1,5$