Question

calcule o valor de x nas seguintes igualdades
$a) \sqrt[10]{ {2}^{8} } = \sqrt[x]{ {2}^{4} }$
$b) \sqrt[15]{ {3}^{5} } = \sqrt[3]{ {3}^{x} }$
$c) \sqrt[8]{ {5}^{4} } = \sqrt{ {5}^{x} }$
$d) \sqrt[16]{ {4}^{x} } = \sqrt[8]{4}$
se se puder mandar o cálculo eu agradeço​

Answer 1

a)

¹⁰√2⁸ = ˣ√2⁴

2⁸ = (ˣ√2⁴)¹⁰

2⁸ = ˣ√2⁴⁰

(2⁸)ˣ = 2⁴⁰

2⁸ˣ = 2⁴⁰ ⇒ corta as bases

8x = 40

x = 40/8

x = 5

________________________

b)

¹⁵√3⁵ = ³√3ˣ

(¹⁵√3⁵)³ = 3ˣ

¹⁵√3¹⁵ = 3ˣ

3 = 3ˣ ⇒ corta as bases

1 = x

x = 1

________________________

c)

⁸√5⁴ = √5ˣ

(⁸√5⁴)² = 5ˣ

⁸√5⁸ = 5ˣ

5 = 5ˣ ⇒ corta as bases

1 = x

x = 1

________________________

d)

¹⁶√4ˣ = ⁸√4

4ˣ = (⁸√4)¹⁶

4ˣ = ⁸√4¹⁶

4ˣ = 4² ⇒ corta as bases

x = 2