Question

$( 3^{x}) ^{x-4} =1/27$
$( \frac{1}{4} ) ^{x-1} = 16^{x-2}$

Answer 1

E aí Nerd1,

use as propriedades da exponenciação:

$(a^m)^n~\to~a^{m*n}~\to~a^{mn}\\\\ \dfrac{1}{a}~\to~ \dfrac{1}{a^1}~\to~a^{-1}$

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$\begin{cases}(3^x)^{x-4}= \dfrac{1}{27}\\\\ \not3^{ x^{2} -4x}=\not3^{-3}\\ x^{2} -4x=-3\\ x^{2} -4x+3=0\\\\ x'=1~~e~~x''=3\\\\ \boxed{S=\{1,3\}}\end{cases}\begin{cases}\left( \dfrac{1}{4}\right)^{x-1}=16^{x-2}\\\\ (2^{-2})^{x-1}=(2^4)^{x-2}\\ \not2^{-2x+2}=\not2^{4x-8}\\ -2x+2=4x-8\\ -2x-4x=-8-2\\ -6x=-10\\\\ x= \dfrac{-10}{-6}\\ x= \dfrac{5}{3}\\\\ \boxed{S=\left\{ \dfrac{5}{3}\right\}}\end{cases}$

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