LOG PROPERTIES
EXPANDING AND CONDENSING WS
NAME ______________________
Expand each of the following using the properties of logs.
1.
log3 6x
2.
log 6 x5
3.
log 5
4.
log 5x 4 y 2
5.
log3 x
6.
log
3y4
8.
log3 5 p
9.
log 4
7.
log
1
4x3
7
3
2
xy
9( x  1)
( x  2)
Condense the following using the properties of logs.
10.
log 2 3  log 2 x
11.
13.
2 log 3  log 5
14.
16.
log 2 x  log 2 y  log 2 3
17.
log5 8  log5 3
log 20  2log y  log z
log 4 ( x  1)  log 4 7  2log 4 y
12.
5log 7 r
15. log 3 2 
1
log 3 y
2
18. log 5  log 3  log x  log y
LOG PROPERTIES – EXPANDING & CONDENSING WS – ANSWERS:
1.
1  log3 2  log3 x
2.
4.
log 5  4log x  2log y
5.
5log 6 x
7.
1
log 3  4 log y  2 log 2  log x
3
9.
2 log4 3  log4 ( x  1)  log4 ( x  2)
10.
log 2 3x
13.
log
16.
log 2
9
5
xy
3
1
log 3 x
2
8.
3.
log5 7  log5 3
6.
log 2  log x  log y
1
1
log3 5  log 3 p
2
2
11.
log 5
8
3
12.
log 7 r 5
14.
log 20y 2 z
15.
log3 2 y
17.
log 4
18.
log
( x  1)
7 y2
5
3xy