College Algebra, 2013a

6.2 Properties of Logarithms 445
6.2.1 Exercises
In Exercises 1 - 15, expand the given logarithm and simplify.
quantities represent positive real numbers.
( ) 128
1. ln(x 3 y 2 ) 2. log 2
x 2 +4
4. log(1.23 × 10 37 ) 5. ln
(√ ) z
xy
Assume when necessary that all
) 3
( z
3. log 5
25
(
6. log 5 x 2 − 25 )
(
7. log √ 2 4x
3 ) 8. log 1 (9x(y 3 − 8)) 9. log ( 1000x 3 y 5)
3
10. log 3
( x
2
81y 4 )
( √ ) 100x y
13. log 3√
10
( √ )
4 xy
11. ln
ez
14. log 1
2
(
4 3√ )
x 2
y √ z
( ) 216 4
12. log 6
x 3 y
( √ 3
) x
15. ln
10 √ yz
In Exercises 16 - 29, use the properties of logarithms to write the expression as a single logarithm.
16. 4 ln(x)+2ln(y) 17. log 2 (x)+log 2 (y) − log 2 (z)
18. log 3 (x) − 2log 3 (y) 19.
1
2 log 3(x) − 2log 3 (y) − log 3 (z)
20. 2 ln(x) − 3ln(y) − 4ln(z) 21. log(x) − 1 3 log(z)+ 1 2 log(y)
22. − 1 3 ln(x) − 1 3 ln(y)+ 1 3 ln(z) 23. log 5(x) − 3
24. 3 − log(x) 25. log 7 (x)+log 7 (x − 3) − 2
26. ln(x)+ 1 2
27. log 2 (x)+log 4 (x)
28. log 2 (x)+log 4 (x − 1) 29. log 2 (x)+log1 (x − 1)
2