Precalculus
9.1 – 9.4 Reveiw
Name_________________________
Per_____
Evaluate.
1)
5
322
2)
1
493
Simplify.
3)
 2x y
4
1
8 2

4) 16x 
1
2
4
 
 x

1
2
1
  x2  4
5)
5 3
x15
y 16
Solve each exponential equation.
x
 1 
7)    23 x5
 64 
6) 9  3
4x
5
8) xe2 x  5e2 x
Graph each function.
1
9) H  x    
3
x
11) f  x   e x
10) g  x   e x  1
Solve for x to the nearest hundredth.
12) log 0.00325  x
13) ln 4255  x
14) ln x  2.22
15) log x  4.0005
Find domain, range, asymptotes, and x- and y-intercepts of each function. Then graph the function.
16) h( x)  log  x  10 
17) p( x)  ln  x  e 
Express each in condensed form.
1
18) log x 2  2log y  log 4
4
19)
2
3
log3 x3  log3 y 4  log3 10
3
4
Express each in expanded form.
20) logb x3 y
21) log b
x2
5 yz
Find the domain, express the equation in equivalent exponential form and solve.
22) log5  6 x  7   log5 x  1
23) 5log3 x  2log3 x  3
Fill in the missing steps in each of the proofs of a property of logarithms.
24)
25)
Let log b M  u and log b N  v
Let log b M  u and log b N  v
Then bu  _____ and bv  _____ .
M N  ________
M N  b
u v
log b M N  ________
log b M N  log b M  log b N
Then bu  _____ and b v  _____ .
M
 ________
N
M
 bu  v
N
M
log b
 ________
N
M
log b
 log b M  log b N
N
26)
Let log b M  u
Then bu  _____
b 
u r
 ________
bur  M r
log b bur  ________
u  r  ________
r  log b M  log b M r