Question

Resolvendo a equação exponencial (3 elevado a 2x-7)³ : 9 elevado a x-1 = (3x elevado a 3x-1) elevado a 4, obtemos:

A. S = {3/14}
B. S = {5}
C. S = {2/5}
D. S = {-19/8}
E. S = { }

Answer 1

Aplique as propriedades da exponenciação:

$(a^m)^n=a^{m\cdot n}\\\\ \dfrac{a^m}{a^n}=a^{m-n}$

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$\dfrac{(3^{2x-7})^3}{9^{x-1}}=(3^{3x-1})^4\\\\ \Rightarrow \dfrac{3^{6x-21}}{(3^2)^{x-1}}=3^{12x-4}\\\\ \Rightarrow \dfrac{3^{6x-21}}{3^{2x-2}}=3^{12x-4}\\\\ \Rightarrow3^{6x-21}:3^{2x-2}=3^{6x-4}\\\\ \Rightarrow3^{6x-2x-21+2}=3^{6x-4}\\\\ \Rightarrow\not3^{4x-19}=\not3^{6x-4}\\\\ \Rightarrow 4x-19=6x-4\\ 4x-6x=-4+19\\ -2x=15\\\\ x=- \dfrac{15}{4}\\\\\\ \text{S}=\left\{- \dfrac{15}{4}\right\}$

Tenha ótimos estudos ;P