Homework Help

Write as an expression of a single logarithm and simplify completlely  3Log(4)3+...

user profile pic

connorcolin3 | Valedictorian

Posted May 9, 2013 at 11:57 PM via web

dislike 1 like

Write as an expression of a single logarithm and simplify completlely 

3Log(4)3+ Log(4)2-1/2log(4)36

Numbers in parthensis are subscripts

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Tagged with al, math

2 Answers | Add Yours

user profile pic

jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted May 10, 2013 at 3:09 AM (Answer #1)

dislike 1 like

To do this we need some basic principles in logarithm.

For positive a,A and B;

`log_aA+Log_aB = log_a(AB)`

`log_aA-Log_aB = log_a(A/B)`

`Plog_aA = log_a(A)^P`

 

`3Log(4)3+ Log(4)2-1/2log(4)36`

`= log_4(3^3)+log_4(2)-log_4(36)^(1/2)`

`= log_4(27)+log_4(2)-log_4(6)`

`= log_4[(27xx2)/6]`

`= log_4(9)`

 

So the answer is ;

`3Log(4)3+ Log(4)2-1/2log(4)36 = log_4(9)`

Sources:

user profile pic

oldnick | Valedictorian

Posted May 10, 2013 at 3:17 AM (Answer #2)

dislike 1 like

`3log_4 3+log_4 2 -1/2 log_4 36=` `=2log_4 3+ log_4 3+log_4 2-1/2log_4(3^2 xx 2^2)=`

`=2log_4 3 +log_4 3xx2 -1/2( log_4 3^2 +log_4 2^2)=`

`=2log_4 3 +log_4 6-1/2(2log_4 3 +2log_4 2)=`

`=2log_4 3+log_4 6 -(log_4 3+ log_4 2)=`

`=2log_4 3 +log_4 6-log_4 3xx2 =`

`=log_4 3 +log_4 6- log_4 6=2log_4 3`

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes