Question

3^x = y² and y^x = 9
Solve for X and Y.
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Answer 1

Answer:

3^x=y^2

√3^x=y

y^x=9

x√9=y

Answer 2

Answer :

(2 , 3) , (2 , -3) , (-2 , ⅓) , (-2 , -⅓)

Solution :

Here ,

The given equations are ;

3^x = y² ------(1)

y^x = 9 -------(2)

Squaring both sides of eq-(2) , we get ;

=> (y^x)² = 9²

=> y^(2x) = 81

=> (y²)^x = 81

=> (3^x)^x = 81

=> 3^(x²) = 81

=> 3^(x²) = 3⁴

=> x² = 4

=> x = √4

=> x = ±2

• If x = 2 , then using eq-(1) , we get ;

=> 3^x = y²

=> 3² = y²

=> 9 = y²

=> y² = 9

=> y = √9

=> y = ±3

• If x = -2 , then using eq-(1) , we get ;

=> 3^x = y²

=> 3^(-2) = y²

=> 1/3² = y²

=> 1/9 = y²

=> y² = 1/9

=> y = √(1/9)

=> y = ±⅓

Hence ,

(2 , 3) , (2 , -3) , (-2 , ⅓) , (-2 , -⅓) are the solutions of the given pair of equations .