The value of x if 3root 9 3root27 3 root 81 3 root 243 is equals to x root 3power x plus 2
Answers
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
Given : ∛9 × ∛27 × ∛81 × ∛ 243 =
To find : Value of x
Solution:
∛9 × ∛27 × ∛81 × ∛ 243 =
=> ∛3² × ∛3³ × ∛3⁴ × ∛ 3⁵ =
=> ∛3⁽²⁺³⁺⁴⁺⁵⁾ =
=> ∛3⁽¹⁴⁾ =
=> 3^(14/3) = 3^(x+2/x)
=> (x + 2)/x = 14/3
=> 3x + 6 = 14x
=> 11x = 6
=> x = 6/11
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