Download log 81 ln e ln e B 1 log (2 5) log ( 3) 2 y y + - + 2log 3log a b - 8 14 6 x- -

Math 1314
TEST #4-Review
.
3. Graph the function and label one “key” point. Find the domain and range. Give equation of the
asymptote.
B. f ( x )  ln( x  4)  3
C. f ( x)  e x  2  4 D. f ( x )  ln( x  2)  1
A. f ( x)  2 x 1  3
Find the exact value of each expression.
4.
log 6 36
8.
8log 11
5.
8
6.
log 3 81
9.
 1 
log 4  
 64 
ln 3 e 2
7.
10.
log 3 4 9
log 49 7
Expand each expression as much as possible. Evaluate where necessary.
11.
 8x 
log 2  
 y 
12.
m5 n 4
t2
log p 3
13.
 7 e4
ln 
 B





Write each expression as a single logarithm with a coefficient of 1.
14.
1
log b (2 y  5)  log b ( y  3)
2
15.
2log m a  3log m b 2
Solve each exponential equation.
16.
2 2 x1  32
17.
52  x 
1
125
18.
e x4 
1
e2 x
Solve each equation. Where necessary, round to the nearest thousandth.
x 2
20. 8  14  6
5 x  21
log 5 ( x  4)  log 5 ( x )  1
25. log 4 (2 x  3)  log 4 x  log 4 ( x  2)
27. 2log x  log 2  log(3 x  4)
19.
23.
21.
24.
26.
28.
1 4 x
4e5 x  16
 21
22. e
log 3 (4 x  10)  log 3 ( x  1)  2
log 9 ( x  5)  log 9 ( x  3)  1
log 7 ( x  1)  log 7 ( x  5)  1
Answers
3. A.
D:
R:
C.
D:
R:
(, )
(3, )
B.
(, )
(,4)
D.
D:
R:
D:
R:
4. 2
5. 8
6. 3
16.
17.
1
7.
2
8. 11
2
9.
3
1
10.
4
18.
11.
21.
12.
13.
14.
15.
3  log 2 x  log 2 y
1
(5log p m  4log p n  2log p t )
3
4
 ln B
7
 2y  5 
log b 
 y  3 


 a2 
log m  6 
b 
19.
20.
22.
23.
24.
25.
26.
27.
28.
x3
x5
4
3
ln 21
x
 1.892
ln 5
ln 20
x
 2  3.441
ln8
ln 4
x
 0.277
5
ln 21  1
 0.511
x
4
x5
1
x
5
x3
x6
x  4,2
x6
x
(4, )
(, )
(2, )
(, )