I NEED A STEP BY STEP EXPLANATION FOR THIS PLEASE....EXPLAIN STEP BY STEP
Answers
Answer:
x = 3/2 , y = 3
Step-by-step explanation:
Given---> 4³ʸ⁻⁴ˣ = 64
3ʸ ÷ 9ˣ = 1
To find---> Value of x and y
Solution---> ATQ,
4³ʸ⁻⁴ˣ = 64
=> 4³ʸ⁻⁴ˣ = 4× 4 × 4
=> 4³ʸ⁻⁴ˣ = 4³
Comparing exponents we get,
=> 3y - 4x = 3 .........................(1)
ATQ, 3ʸ ÷ 9ˣ = 1
=> 3ʸ ÷ ( 3² )ˣ = 1
We have a law of exponent,( aᵐ)ⁿ = aᵐⁿ , applying it here we get
=> 3ʸ ÷ 3²ˣ = 1
We have some law of exponent
aᵐ ÷ aⁿ = aᵐ⁻ⁿ , and a⁰ = 1 , applying it we get
=> 3ʸ⁻²ˣ = 3⁰
on comparing exponent we get
=> y - 2x = 0
=> y = 2x ............................(2)
Putting y = 2x in equation (1) we get
=> 3 ( 2x ) - 4x = 3
=> 6x - 4x = 3
=> 2x = 3
=> x = 3 / 2
Putting x = 3/2 in equation (2) , we get
=> y = 2x
=> y = 2 ( 3 / 2 )
=> y = 3
So, x = 3/2 , y = 3
x3/2,y=3
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