Question

Exponencial


(3^x)^x-1 = 9

Answer 1

3^x)^x-1 = 9

3^x)^x-1 = 3²

 x(x-1) = 2
 x² - x - 2 = 0

 Δ= (-1)² - 4.1.(-2)= 1 + 8 = 9

x = 1 +/- √9 ==> x = 1+/- 3
         2.1                     2

x1 = 1 + 3 ==> x1 = 2
          2

x2 = 1- 3 ==> x2 = - 1
          2

Answer 2

$(3 ^{x}) ^{x-1}=9\\ 3 ^{x(x-1)}=3 ^{2}\\ \not3 ^{ x^{2} -x}=\not3 ^{2}\\ \\ x^{2} -x=2\\ x^{2} -x-2=0\\ \\ \boxed{\Delta=b ^{2}-4ac}~\to~\Delta=(-1) ^{2}-4*1*(-2)~\to~\Delta=9\\\\ \boxed{x= \frac{-b\pm \sqrt{\Delta} }{2a}}~\to~x= \frac{-(-1)\pm \sqrt{9} }{2*1}~\to~\begin{cases}x'= \frac{1-3}{2}~\to~x'=-1\\ x''= \frac{1+3}{2}~\to~x''=2 \end{cases}\\ \\\\ Portanto:\\\\ \boxed{\boxed{S=\{-1,~2\}}}$


Espero ter ajudado e tenha ótimos estudos :)