Homework Help

If `log_x(1/4) = -2/3` what is x

user profile pic

asicannot | Student, Kindergarten | eNoter

Posted June 4, 2012 at 6:19 PM via web

dislike 2 like

If `log_x(1/4) = -2/3` what is x

Tagged with equation, exponent, logarithm, math

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted June 4, 2012 at 6:25 PM (Answer #1)

dislike 1 like

x has to be determined given that `log_x(1/4) = -2/3 `

`log_x(1/4) = -2/3`

=> `(1/4) = x^(-2/3)`

=> `(1/8)^(2/3) = x^(-2/3)`

=> `8^(-2/3) = x^(-2/3)`

As the base is the same equate the exponent.

=> 8 = x

The solution of the equation is x = 8

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes