Question

ayudenme porfa es para algebra

Answer 1

Ejercicio 22
$\sqrt[7]{\dfrac{5^{16}+5^x}{5^x+5^2}}=5\\ \\ \\ \dfrac{5^{16}+5^x}{5^x+5^2}=5^7\\ \\ \\ 5^{16}+5^x=5^7(5^x+5^2)\\ \\ 5^{16}+5^x=5^{x+7}+5^{9}\\ \\ 5^{x+7}-5^x=5^{16}-5^9\\ \\ 5^{x}(5^7-1)=5^9(5^7-1)\\ \\ 5^x=5^9\\ \\ \boxed{x=9}$

Ejercicio 23
$\sqrt[4]{\dfrac{7^{10}+7^x}{7^x+7^2}}=7\\ \\ \\ \dfrac{7^{10}+7^x}{7^x+7^2}=7^4\\ \\ \\ 7^{10}+7^x=7^4(7^x+7^2)\\ \\ 7^{10}+7^x= 7^{x+4}+7^6\\ \\ 7^{x+4}-7^x=7^{10}-7^6\\ \\ 7^x(7^4-1)=7^6(7^4-1)\\ \\ 7^x=7^6\\ \\ \boxed{x=6}$