Homework Help

Is `log_5 3` equal to `log_3 5` ?

user profile pic

lkballer24 | Student, Grade 11 | Valedictorian

Posted May 27, 2013 at 2:37 AM via web

dislike 1 like

Is `log_5 3` equal to `log_3 5` ?

Tagged with math

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 27, 2013 at 2:50 AM (Answer #1)

dislike 1 like

It has to be evaluated if `log_3 5 = log_5 3` .

Use the relation `log_a b = (log_x b)/(log_x a)`

Expressing `log_3 5` and `log_5 3` as an expression with a logarithm that has the same base:

`log_3 5 = (log_10 5)/(log_10 3)` ...(1)

`log_5 3 = (log_10 3)/(log_10 5)` ...(2)

From (1) and (2) it is seen that `log_3 5 != log_5 3` but rather `log_3 5 = 1/(log_5 3)`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes