Question

determine o valor de x em cada caso​

Answer 1

a)

$\sqrt[12]{ {2}^{8} } = \sqrt[x]{ {2}^{2} } \\ \\ {2}^{ \frac{8}{12} } = {2}^{ \frac{2}{x} } \\ \\ {2}^{ \frac{8 \div 4}{12 \div 4} } = {2}^{ \frac{2}{x} } \\ \\ {2}^{ \frac{2}{3} } = {2}^{ \frac{2}{x} } \\ \\ x = 3$

b)

$\sqrt[10]{ {3}^{15} } = \sqrt[x]{ {3}^{3} } \\ \\ {3}^{ \frac{15}{10} } = {3}^{ \frac{3}{x} } \\ \\ {3}^{ \frac{15 \div 5}{10 \div 5} } = {3}^{ \frac{3}{x} } \\ \\ {3}^{ \frac{3}{2} } = {3}^{ \frac{3}{x} } \\ \\ x = 2$

c)

$\sqrt[27]{512} = \sqrt[3]{ {2}^{x} } \\ \\ \sqrt[27]{ {2}^{9} } = \sqrt[3]{ {2}^{x} } \\ \\ {2}^{ \frac{9}{27} } = {2}^{ \frac{x}{3} } \\ \\ {2}^{ \frac{9 \div 9}{27 \div 9} } = {2}^{ \frac{x}{3} } \\ \\ {2}^{ \frac{1}{3} } = {2}^{ \frac{x}{3} } \\ \\ x = 1$