Logarithms (Sec. 5.3 and 5.4)
Answer True or False for 1 – 11.
_______ 1.
y  log 4 x is the inverse of y  4 x
_______ 2.
y  log 4 x is equivalent to 4 y  x
_______ 3.
You can take a log of a negative number.
_______ 4.
The value (output) of a log can be a negative number.
_______ 5.
log 2 0  1
_______ 6.
log a ( y  4)  log a y  log a 4
_______ 7.
log a w
1
log a w1/ 3  log a w 
3
3
_______ 8.
 loga w 
_______ 9.
log a t 5
5
log a t
3
 3log a w
_______ 10. If 0  N  1 , then log N  0 .
1
_______ 11. If log(1/ 4) x  3 , then log 4    3
x
Find a formula for f 1 ( x) . Also state the domain and range of f and f 1 .
12.
f ( x)  7 x
13.
f ( x)  e x
14.
f ( x)  log 5 x
15.
f ( x)  ln x
Given log b 2  w , log b 3  x, log b 5  y , and log b 7  z , write each of the following in
terms of w, x, y, and z.
16. log b 250
17.
27
log b  
 49 
18.
30
log b  
 7b 
Express each of the following in terms of log a, log b, and log c . All logarithms in 19 – 21
are common logs.
 c5 
19. log 

3 2
 b a
20.
log 4
c2  b
a
21. log 10log a  10log b  10log c 
Write each as a single log.
22. log a 4  log a   3log a r  log a 3
23. log(w  1)  log(w  1)  log  w2  w  1  log  w3  1  log  w2  1
24. M  4logb  bM   2logb M  logb  bM k 
Answers to Logarithms
1. T
2. T
7. T
8. F
12.
3. F
9. T
f 1 ( x)  log 7 x
4. T
5. F
10. T
11. T
dom f : All real numbers
dom f 1 :
13.
f 1 ( x)  ln x
range f :
f 1 ( x)  5 x
dom f :
0, 
range f :
f 1 ( x)  e x
dom f :
0, 
range f : All real numbers
0, 
17. 3x  2z
range f 1 :  0, 
range f : All real numbers
dom f 1 : All real numbers
16. w  3 y
0, 
range f 1 : All real numbers
dom f 1 : All real numbers
15.
0, 
range f 1 : All real numbers
dom f : All real numbers
dom f 1 :
14.
0, 
6. F
range f 1 :  0, 
18. w  x  y  z  1
2
1
19. 5log c  log b  log a
3
3
20.
1
1
1
log c  log b  log a
2
8
4
21. log a  log b  log c
22.
 4 r 3 
log a 

 3 
23. log( w  1)
24.
1
log b  4 2  or  log b  b4 M 2 k 
b M k