Question

The value of x if 3root 9 3root27 3 root 81 3 root 243 is equals to x root 3power x plus 2​

Answer 1

Answer:

0.2  

Step-by-step explanation:

⇒ 3√9 . 3√27 . 3√81 . 3√243

⇒ 3.3.3.3  . √9.√27.√81.√243

⇒ 3⁴ . √(3²) . √(3².3) . √(9²) . √(9².3)

⇒ 3⁴ . (3) . (3√3) . (9) . (9√3)

⇒ 3⁴ . 3 . 3 . 9 . 9 . (√3 . √3)

⇒ 3⁴⁺¹⁺¹ . 3² . 3² . 3

⇒ 3⁶⁺²⁺²⁺¹

⇒ 3¹¹     Which is said as xth root3 ^(x+2)

        Now,

⇒ 3¹¹ = { 3^(x+2) }^(1/x)

⇒ 3¹¹ = 3^(x+2)/x

⇒ 11 = (x + 2)/x

⇒ 11x = x + 2

⇒ 10x = 2

⇒ x = 2/10 = 0.2

Answer 2

Given :  ∛9 × ∛27 × ∛81 ×  ∛ 243  = $\sqrt[x]{3^{x+2}}$

To find : Value of x

Solution:

∛9 × ∛27 × ∛81 ×  ∛ 243  = $\sqrt[x]{3^{x+2}}$

=> ∛3² × ∛3³ × ∛3⁴ ×  ∛ 3⁵  = $\sqrt[x]{3^{x+2}}$

=> ∛3⁽²⁺³⁺⁴⁺⁵⁾ = $\sqrt[x]{3^{x+2}}$

=>  ∛3⁽¹⁴⁾ = $\sqrt[x]{3^{x+2}}$

=>  3^(14/3) = 3^(x+2/x)

=> (x + 2)/x = 14/3

=> 3x + 6  = 14x

=> 11x = 6

=> x = 6/11

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