4.14
Properties of Logarithmic Functions
Name _________________________________________ Date ________________ Period _____________
Assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
5
y
1. ln 4x
2. ln 27y
3. log
6
x
5. log y 4
6. log3 x 2
8. log x3 y
9. ln
y
x
12. ln
4. log
7. log x 2 y 3
10. log10000x3
11. log 4
x3
y2
3
3
y
x
Assuming x, y and z are positive, use properties of logarithms to write the expression as a single logarithm.
13. log x  log z
14. log y  log 7
15. ln x  ln 5
16. ln y  ln x
17.
1
ln y
2
18.
1
ln z
4
19. 3ln z  2 ln x
20. 2 log x  log y
21. 3log ( xy)  2 log ( yz)
22. 2 ln ( x2 y)  3ln ( yz3 )
Use the change-of-base formula and your calculator to evaluate the logarithm. Show work!
23. log3 5
24. log4 18
25. log6 159
26. log13 236
27. log0.5 15
28. log0.2 34
Write the expression using only natural logarithms.
29. log4 x
30. log8 x
31. log3  x  y 
32. log5  a  b
Write the expression using only common logarithms.
33. log3 x
34. log5 x
35. log1 3  x  y 
36. log1 2  x  y 
Solve.
38. 37 x  272 x1
37. 43  8x1
x3
39. 125
 25
3x
40.
1
 
4
2
 82 x1