Question

Gente me ajudem a resolver essa questão, eu to meio confusa:
25(elevado a x) = 6 x 5(elevado a x) - 5

Answer 1

Oi Bianca,

use uma das propriedades da exponenciação, acompanhe a resolução:

$\mathsf{25^x=6\cdot5^x-5}\\ \mathsf{(5^2)^x-6\cdot5^x+5=0}\\ \mathsf{(5^x)^2-6\cdot5^x+5=0}\\\\ \mathsf{5^x=y}\\\\ \mathsf{y^2-6y+5=0}\\\\ \mathsf{\Delta=(-6)^2-4\cdot1\cdot5}\\ \mathsf{\Delta=36-20}\\ \mathsf{\Delta=16}\\\\ \mathsf{y= \dfrac{-(-6)\pm \sqrt{16} }{2\cdot1} = \dfrac{6\pm4}{2} }\begin{cases}\mathsf{y_1= \dfrac{6-4}{2}= \dfrac{2}{2}=1 }\\\\ \mathsf{y_2= \dfrac{6+4}{2} = \dfrac{10}{2} =5}\end{cases}$

$\mathsf{5^x=y, ~Lembra?}\\\\ \mathsf{5^x=1}~~~~~~~~~~~~~~~~~~\mathsf{5^x=5}\\ \mathsf{5^x=5^o}~~~~~~~~~~~~~~~~~\mathsf{5^x=5^1}\\ \mathsf{\not5^x=\not5^o}~~~~~~~~~~~~~~~\mathsf{\not5^x=\not5^1}\\\\ \mathsf{~~x_1=0}~~~~~~~~~~~~~~~~~~\mathsf{x_2=1}\\\\\\ \Large\boxed{\mathsf{S=\{0,1\}}}$

Se tiver dúvidas me chame. Tenha ótimos estudos! :))