Question

Resolva as equações exponenciais determinando os correspondentes valores de x.
A-7^(x-3)+7^(x-2)+7^(x-1)=57

Answer 1

$\boxed{\mathrm{7^{(x-3)}+7^{(x-2)}+7^{(x-1)}=57}}\\\\ \mathrm{\dfrac{7^x}{7^3}+\dfrac{7^x}{7^2}+\dfrac{7^x}{7}=57\ \to\ \dfrac{7^x+7.7^x+7^2.7^x}{7^3}=57}\\\\ \mathrm{\dfrac{7^x(1+7+7^2)}{7^3}=57\ \to\ \dfrac{57.7^x}{7^3}=57}\\\\ \mathrm{\dfrac{7^x}{7^3}=\dfrac{57}{57}\ \to\ \dfrac{7^x}{7^3}=1\ \to\ 7^{(x-3)}=7^0}\\\\ \mathrm{Comparando\ os\ expoentes:}\\\\ \mathrm{x-3=0\ \to\ \boxed{\mathbf{x=3}}}$