Math, asked by Anushua2007, 28 days ago

Find the value of x
(3^{-1} + 6^{-1} + 9^{-1} + 12^{-1})^{x} = \frac{36}{25}

Answers

Answered by MonoranjanDas
1

Answer:

x =1

Step-by-step explanation:

sol {}^{n}

(3 {}^{ - 1}  + 6 {}^{ - 1}  + 9 {}^{ - 1}  + 12 {}^{ - 1} ) {}^{x}  =  \frac{25}{36}

 = >  ( \frac{1}{3}  +  \frac{1}{6}  +  \frac{1}{9}  +  \frac{1}{12} ) {}^{x}  =  \frac{25}{36}

 = >  ( \frac{12 + 6 + 4 + 3}{36} ) {}^{x}  =  \frac{25}{36}

 =  > ( \frac{25}{36} ) {}^{x}  = ( \frac{25}{36} ) {}^{1}

so, x=1

Answered by varadad25
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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