6.3-6.5 Review
In #1-10, evaluate the logarithm without a calculator (show work):
1. log 9 81

6. log 10 10

2. log 8 1
3. log 3 ( 13 )
4. log 27 3
5. log 10−9
7. log 8 4
8. log 16  12 
9. log 25 125
10. 4𝑙𝑛𝑒 7
11. Use a calculator to evaluate each logarithm to the nearest thousandth:
a) 1  ln 7
b)
log 82
0.24
c)
ln 15
2  ln 10
12. Find the inverse of the function. (Simplify your answers.)
a) y  log 6 x  2
d) y  ln x 1  3
c) y  log 1 2 x   3
2
b) y  log 3 4 x
e) y  log 2 8 x 1
13. (no calc.) Graph the function. Give four ordered pairs. State the domain and range. Give the equation of any
asymptotes:
a) y  log 3 x
x y
Domain:
Range:
Asymptote:
b) y  log 2 x  2
x
y
Domain:
Range:
Asymptote:
14. Describe the transformation of f represented by g.
a. f  x  2 x , g  x  2 x  3 b. f  x  e x , g  x  e x  4
c.
f  x   3x , g  x    3 x  2
e. f  x  log 2 x, g  x  4 log 2 x  1
d.
f  x  e x , g  x  2e 5 x
f.
f  x  log1 2 x, g  x   log1 2 x  3
15. Write a rule for g that represents the indicated transformation of the graph of f.
a.
f  x  3x ; reflection in the x-axis, followed by a translation 3 units left and 1 unit down
b.
f  x  e x ; vertical shrink by a factor of 1 , followed by a translation 5 units up
c.
f  x  log8 x ; reflection in the y-axis, followed by a translation 4 units left
d.
f  x  log1 6 x ; vertical stretch by a factor of 9, followed by translations 2 units right and 3 units down
4
16. Match the expression with the logarithm that has the same value (show simplifying work):
a) log 2  log 8
i. log
b) log 4  log 10
ii. log 27
c) 2 log 4  log 2
iii. log 4
d)  3 log  13 
iv. log 8
2
5
17. (no calc) Use log 4  0.60 and log 7  0.85 to evaluate the logarithm: (Show your work)
a) log 28
b) log  74 
c) log 16
d) log 49
e) log  14 
49

f) log  64
18. (no calc) Use ln 2  0.69 and ln 3  1.10 and ln 7  1.95 to evaluate the logarithm: (Show your work)
a) ln 16
c) ln  21

4
b) ln 42
19. Expand the expression (and simplify where
possible):
a) log 12 x 3 =
20. Condense the expression:
a) log 3  12 log x  log 5 =
 5x 3 
 =
b) log 6 
6


b) log 4  3 log x  log y =
c) log 3 x  2  log 3 5 =
 2x 

c) log 2 
 2  =




d) ln  24
9
d) 2 log x  log x  4 =

5
d) log 9 2 x 2 yz =

e) ln 5  x
3

e) 2log 2 3  12 log 2 x   log 2 y  4 log 2 x =
=
21. Use your calculator to evaluate each logarithm to three decimal places:
a) log 7 19 
b) log 15 158 