We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
151
1
avatar+1055 

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.

 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

 Aug 2, 2018
edited by Guest  Aug 2, 2018

8 Online Users

avatar
avatar