Question

Решите показательное уравнение:

Answer 1

$\displaystyle\sf 2^{x^2-1}+3^{x^2-1}=3^{x^2+1}-13\cdot 2^{x^2}\\2^{x^2-1}+13\cdot 2^{x^2}=3^{x^2+1}-3^{x^2-1}\\2^{x^2}\cdot \frac{1}{2}+13\cdot 2^{x^2}=3^{x^2}\cdot 3-3^{x^2}\cdot \frac{1}{3}\\\\2^{x^2}\cdot \frac{27}{2}=3^{x^2}\cdot \frac{8}{3}|:\frac{27}{2}\\\\2^{x^2}=3^{x^2}\cdot \frac{16}{81}|:3^{x^2}\\\\(\frac{2}{3})^{x^2}=\frac{16}{81}\\\\(\frac{2}{3})^{x^2}=(\frac{2}{3})^4\\\\x^2=4\\\\ \left [{ {{x=2} \atop {x=-2}} \right.$

Ответ: $-2;2$