Homework Help

What is a if log(base3)2+log(base3)a=1?

user profile pic

yapayapa | Honors

Posted September 19, 2013 at 3:51 PM via web

dislike 1 like

What is a if log(base3)2+log(base3)a=1?

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 19, 2013 at 4:00 PM (Answer #1)

dislike 1 like

You need to convert the summation of logarithms into the logarithm of product, such that:

`log_3 2 + log_3 a = log_3 (2a)`

Since `log_3 2 + log_3 a = 1` , you need to replace `log_3 (2a)` for `log_3 2 + log_3 a,` such that:

`log_3 (2a) = 1 => 2a = 3^1 => a = 3/2`

Since a is the argument of logarithms, it needs to be positive, hence, `a = 3/2 ` is valid.

Hence, evaluating the value of a, under the given conditions, yields `a = 3/2.`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes