Math, asked by tauhidjagirdar7456, 11 months ago

If (27)^x=(81)^y then 3x-4y=?

Answers

Answered by rishu6845

Answer:

3x - 4y = 0

Step-by-step explanation:

Given----> ( 27 )ˣ = ( 81 )ʸ

To find ---> Value of 3x - 4y

Solution ---> First we find prime factorization of 27 and 81

27 = 3 × 3 × 3

81 = 3 × 3 × 3 × 3

Now , ATQ,

( 27 )ˣ = ( 81 )ʸ

=> ( 3 × 3 × 3 )ˣ = ( 3 × 3 × 3 × 3 )ʸ

We have a law of exponent as follows

aᵐ aⁿ = aᵐ⁺ⁿ , applying it here , we get

=> ( 3³ )ˣ = ( 3⁴ )ʸ

=> 3³ˣ = 3⁴ʸ

Since base of both sides are same so comparing exponent from both sides we get

=> 3x = 4y

=> 3x - 4y = 0

So value of 3x - 4y is equal to zero

Additional information--->

1) aᵐ / aⁿ = aᵐ⁻ⁿ

2) aᵐ bᵐ = ( a b )ᵐ

3) 1 / aᵐ = a⁻ᵐ

4) a⁰ = 1

5) ( aᵐ )ⁿ = aᵐⁿ

Answered by Aɾꜱɦ

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3x-4y=0

#answerwithquality #bal

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