Question

Решите показательные уравнения: 6^x-2-(1/6)^3-x+36^x-1/2=246 (0,8)^3-2x=(1,25)^3

Answer 1

$6^{x-2} - (\frac16)^{3-x}+36^{\frac{x-1}{2}} = 246\\\\ \frac{6^x}{36} - 6^{x-3}+6^{x-1} = 246\\\\ \frac{6^x}{36} - \frac{6^x}{216}+\frac{6^x}{6} = 246\\\\ 6^x = t, t \ \textgreater \ 0\\ \frac{t}{36} - \frac{t}{216}+\frac{t}{6} = 246\\\\ 6t-t+36t = 53136\\ 41t=53136\\ t = 1296\\\\ 6^x = 1296\\ 6^x = 6^4\\ x=4$