Question

Resolva a equacao exoonencial: (2^x-3)^x-2=1

Answer 1

EAE manoo,

use as propriedades da exponenciação..

$\boxed{(a^m)^n\Rightarrow a^{m\cdot n}\Rightarrow a^{mn}}\\\\ \boxed{1=a^o}$

$(2^{x-3})^{x-2}=1\\ (2^{(x-3)\cdot(x-2)})=2^0\\ \not2^{x^2-2x-3x+6}=\not2^0\\\\ x^2-5x+6=0\\\\ \Delta=(-5)^2-4\cdot1\cdot6\\ \Delta=25-24\\ \Delta=1\\\\ x= \dfrac{-(-5)\pm \sqrt{1} }{2\cdot1}= \dfrac{5\pm1}{2}\begin{cases}x'=2\\ x''=3\end{cases}\\\\\\ \huge\boxed{\boxed{S=\{2,~3\}}}$

Tenha ótimos estudos ;D