Homework Help

Solve the equation (9^log x)^2 = 81^(log y)

user profile pic

lxsptter | Student, Undergraduate | (Level 2) Valedictorian

Posted July 3, 2013 at 2:33 PM via web

dislike 2 like

Solve the equation (9^log x)^2 = 81^(log y)

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 3, 2013 at 2:38 PM (Answer #1)

dislike 2 like

The equation `(9^log x)^2 = 81^(log y)` has to be solved.

It should be noted that the equation has two variables x and y. As a result it is not possible to find a unique solution. Only an expression for one of the variables in terms of the other can be determined.

`(9^log x)^2 = 81^(log y)`

=> `9^(2*log x) = (9^2)^(log y)`

=> `9^(2*log x) = 9^(2*log y)`

As the base is the same, the exponent can be equated.

=> `2*log x = 2*log y`

=> `x = y`

The relation between x and y derived from the given equation is y = x.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes