Question

alguém me ajuda a resolver?? por favor

Answer 1

Boa noite!

$7^m-3^{2n}=1672\\ \left(\sqrt{7}\right)^{2m}-3^{2n}=1672\\ \left[\left(\sqrt{7}\right)^m-3^n\right]\left[\left(\sqrt{7}\right)^m+3^n\right]=1672\\ 22\left[\left(\sqrt{7}\right)^m+3^n\right]=1672\\ \left[\left(\sqrt{7}\right)^m+3^n\right]=\frac{1672}{22}\\ \left[\left(\sqrt{7}\right)^m+3^n\right]=76$

Somando e subtraindo agora as duas equações:
$\left[\left(\sqrt{7}\right)^m+3^n\right]=76\\ \left[\left(\sqrt{7}\right)^m-3^n\right]=22\\ 2\sqrt{7^m}=76+22\\ \sqrt{7^m}=49\\ 7^{\frac{m}{2}}=7^2\\ \frac{m}{2}=2\\ m=4\\ 2(3^n)=76-22\\ 3^n=27\\ 3^n=3^3\\ n=3\\ m^n=4^3=64$

Espero ter ajudado!