Find the value of x
( + + + ) =
Answers
Answered by
1
Answer:
x =1
Step-by-step explanation:
so, x=1
Answered by
1
Answer:
The value of x is - 1.
Step-by-step-explanation:
The given equation is
( 3⁻¹ + 6⁻¹ + 9⁻¹ + 12⁻¹ )ˣ = 36 / 25
We have to find the value of x.
Now,
( 3⁻¹ + 6⁻¹ + 9⁻¹ + 12⁻¹ )ˣ = 36 / 25
We know that,
a⁻ᵐ = 1 / aᵐ
⇒ [ ( 1 / 3 ) + ( 1 / 6 ) + ( 1 / 9 ) + ( 1 / 12 ) ]ˣ = 36 / 25
⇒ { [ ( 6 + 3 ) / 18 ] + [ ( 12 + 9 ) / 108 ] }ˣ = 36 / 25
⇒ [ ( 9 / 18 ) + ( 21 / 108 ) ]ˣ = 36 / 25
⇒ [ ( 972 + 378 ) / 1944 ]ˣ = 36 / 25
⇒ ( 1350 / 1944 )ˣ = 36 / 25
⇒ ( 150 / 216 )ˣ = 36 / 25
⇒ ( 50 / 72 )ˣ = 36 / 25
⇒ ( 25 / 36 )ˣ = 36 / 25
⇒ ( 25 / 36 )ˣ = 1 / ( 25 / 36 )
We know that,
1 / aᵐ = a⁻ᵐ
⇒ ( 25 / 36 )ˣ = ( 25 / 36 )⁻¹
As the bases are equal, powers must be equal.
⇒ x = - 1
∴ The value of x is - 1.
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