Question

equação exponencial (3x)2x-7=1/27

Answer 1

Olá Carolina,

use as propriedades da exponenciação:

$(3^x)^{2x-7}= \dfrac{1}{27}\\\\ 3^{2x^2-7x}= \dfrac{1}{3^3}\\\\ \not3^{2x^2-7x}=\not3^{-3}\\\\ 2x^2-7x=-3\\ 2x^2-7x+3=0\\\\ \Delta =b^2-4ac\\ \Delta=(-7)^2-4\cdot2\cdot3\\ \Delta=49-24\\ \Delta=25\\\\ x= \dfrac{-(-7)\pm \sqrt{25} }{2\cdot2}= \dfrac{7\pm5}{4}\begin{cases}x_1= \dfrac{7-5}{4}= \dfrac{2}{4}= \dfrac{1}{2}\\\\ x_2= \dfrac{7+5}{4}= \dfrac{12}{4}=3 \end{cases}\\\\\\ \Large\boxed{\text{S}=\left\{ \dfrac{1}{2},~3\right\}}$

Tenha ótimos estudos ;P