+0  
 
0
67
1
avatar+753 

If $3^{x + y} = 81$ and $81^{x - y} = 3,$ then what is the value of the product $xy$? Express your answer as a common fraction.

Lightning  Aug 2, 2018
 #1
avatar
+1

  3^{x + y} = 81, 81^{x - y} = 3, solve for x, y

 

3^(x +y) =3^4.................(1)

 

3^(4x - 4y) =3^1.............(2)

Equate the exponents on both equations:

(x + y) =4.......................(3)

(4x - 4y) = 1...................(4)

From (3) above:

x = 4 - y   sub this into (4) above

4(4 - y) - 4y = 1

16 - 4y - 4y = 1

16 - 8y = 1

15 - 8y = 0

15 = 8y

y = 15/8 =1 7/8, and x =17/8 =2 1/8

x*y =17/8 * 15/8 =255/64

Guest Aug 2, 2018
edited by Guest  Aug 2, 2018

38 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.