Question

determine o valor de x em cada uma das alternativas:​

Answer 1

a)

$\sqrt[14]{ {2}^{8} } = \sqrt[x]{ {2}^{4} } \\ {2}^{ \frac{8}{14} } = {2}^{ \frac{4}{x} } \\ \frac{8}{14} = \frac{4}{x} \\ 8x = 14 \times 4 \\ 8x = 56 \\ x = \frac{56}{8} \\ x = 7$

b)

$\sqrt[8]{ {5}^{4} } = \sqrt{ {5}^{x} } \\ {5}^{ \frac{4}{8} } = {5}^{ \frac{x}{2} } \\ \frac{4}{8} = \frac{x}{2} \\ 4 \times 2 = 8x \\ 8x = 8 \\ x = \frac{8}{8} \\ x = 1$

c)

$\sqrt[20]{ {7}^{4} } = \sqrt{ {7}^{x} } \\ {7}^{ \frac{4}{20} } = {7}^{ \frac{x}{2} } \\ \frac{4}{20} = \frac{x}{2} \\20x = 4 \times 2\\ 20x = 8 \\ x = \frac{8}{20} \\ x = \frac{2}{5}$

d)

$\sqrt[15]{ {10}^{5} } = \sqrt[3]{ {10}^{x} } \\ {10}^{ \frac{5}{15} } = {10}^{ \frac{x}{3} } \\ \frac{5}{15} = \frac{x}{3} \\ 15x = 5 \times 3 \\ 15x = 15 \\ x = \frac{15}{15} \\ x = 1$

e)

$\sqrt[10]{ {6}^{x} } = \sqrt[5]{6} \\ {6}^{ \frac{x}{10} } = {6}^{ \frac{1}{5} } \\ \frac{x}{10} = \frac{1}{5} \\ 5x = 10 \times 1 \\ 5x = 10 \\ x = \frac{10}{5} \\ x = 2$