Question

Resolva a equação:


(4^2x)^x+3/2 = 1024

Answer 1

Olá Rili,

dada a equação exponencial,

$(4^{2x})^{x+ \tfrac{3}{2} }=1024$

use a propriedade da exponenciação:

$(a^m)^{n}~\to~a^{m.n}~\to~a^{mn}$

__________________________

$4^{2x*(x+ \tfrac{3}{2}) }=4^5\\ \not4^{2 x^{2} + \tfrac{6}{2}x }=\not4^5\\\\ 2 x^{2} + \dfrac{6}{2}x=5\\\\ 2 x^{2} +3x=5\\ 2 x^{2} +3x-5=0$

$\Delta=b^2-4ac\\ \Delta=3^2-4*2*(-5)\\ \Delta=9+40\\ \Delta=49$

$x= \dfrac{-b\pm \sqrt{\Delta} }{2a}\\\\ x= \dfrac{-3\pm \sqrt{49} }{2*2}= \dfrac{-3\pm7}{4}\begin{cases}x'= \dfrac{-3+7}{4}= \dfrac{4}{4}=1\\\\ x''= \dfrac{-3-7}{4}= \dfrac{-10}{~~4}=- \dfrac{5}{2} \end{cases}\\\\\\ S=\left\{1,- \dfrac{5}{2}\right\}$

Espero ter ajudado e tenha ótimos estudos =))