Expanding Logarithms
Name: ________________________________
Date: _____________
Version 1
Score: ________________
Direction: Simplify by expanding the logarithmic expressions. Show all your answer in the space provided.

1) log3 27xy 2

2) log 2 16x8 y 4 z 2
 81 x 
3) log3 
 y 


 36 x 
4) log 6 
 4 y 


Copyright © 2011 ChiliMath
All rights reserved
http://www.chilimath.com
1)
log 3  27 xy 2   log 3  33 xy 2 
 log 3  33   log 3 ( x)  log 3 ( y 2 )
 3log 3 (3)  log 3 ( x)  2 log 3 ( y )
log 3  27 xy 2   3  log 3 ( x)  2 log 3 ( y )
2)
1
4 2 2
log 2 16 x y z  log 2 16 x y z
8
4 2
8

1
log 2 (24 )  log 2 ( x8 )  log 2 ( y 4 )  log 2 ( z 2 ) 
2
1
  4  8log 2 ( x)  4 log 2 ( y )  2 log 2 ( z ) 
2

log 2 16 x8 y 4 z 2  2  4 log 2 ( x)  2 log 2 ( y )  log 2 ( z )
3)
 81 x 
log 3 
 log 3 (81)  log 3
 y 


 x   log  y 
3
 12 
 12 
 log 3  3   log 3  x   log 3  y 
 
 
4
 81 x 
1
1
log 3 
 4  log 3 ( x)  log 3 ( y )
 y 
2
2


4)
 36 x 
 1
 1
log 6 
 log 6  62   log 6  x 2   log 6  y 4 

 4y 
 
 


 1
 1
 2 log 6  6   log 6  x 2   log 6  y 4 
 
 
 36 x 
1
1
log 6 
 2  log 6  x   log 6  y 
 4 y 
2
4

