Homework Help

Show that `1/(log6 a) + 1/(log4 a) = 1/(log24 a)`

user profile pic

shayaan | Student, Undergraduate | (Level 1) Honors

Posted December 3, 2012 at 12:18 PM via web

dislike 0 like

Show that `1/(log6 a) + 1/(log4 a) = 1/(log24 a)`

1 Answer | Add Yours

user profile pic

tiburtius | High School Teacher | (Level 3) Associate Educator

Posted December 3, 2012 at 1:21 PM (Answer #1)

dislike 1 like

We will use formula for change of base:


So we have:

`1/(log_6 a)+1/(log_4 a)=1/((log_(24) a)/(log_(24) 6))+1/((log_(24)a)/(log_(24) 4))=(log_24 6)/(log_24 a)+(log_24 4)/(log_24 a)=(log_24 6+log_24 4)/(log_24 a)`

Now we use formula for logarithm of product:

`log_b(xy)=log_b x+log_b y`

So our expression is equal to:

`(log_24(6cdot4))/(log_24 a)=(log_24 24)/(log_24 a)=1/(log_24 a)`

For more on logarithms see the ling below.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes