Math 3
CHAPTER 4 TEST
Name:_______________________________________________
Evaluate the exponential expression.
1) - 272/3
- 32
-9
Find the value of the logarithmic function.
2) log (0.001)
log (10-3 )
-3
3) log 8 (32)
32 = 8 x
25 = 23 x
25 = 2 3x
5 = 3x
5
=x
3
Graph the function.
(x + 2)
1
4) y = · 4
2
1
1
5)
y = 3log1/6 (x + 4)
Solve the problem.
6) If $4000 is invested in an account that pays interest compounded continuously, how long will it take to grow to
$5100 at 5%? Round to the nearest tenth.
5100 = 4000e.05t
5100
= e.05t
4000
ln
51
= .05t
40
ln
51
40
.05
t
=t
4.9
Find the domain and range of the function.
7) f(x) = 2 log5 (x)
domain: 0,
range: -
,
Rewrite the given equation as an equivalent exponential equation, then solve, round to four decimal places.
8) ln x = 9
e9 = x
x
8103.0839
2
Find the inverse of the function.
9)
-x
f(x) = e + 5
y = e -x + 5
x = e -y + 5
x - 5 = e -y
ln x - 5 = - y
y = - ln x - 5
f-1 x = - ln x - 5 = ln x - 5 -1 = ln
1
x-5
any of these would be acceptable
Solve the equation. If necessary, round to thousandths.
10) 3
(12 - 2x)
= 729
3(12 - 2x) = 3 6
12 - 2x = 6
-2x = -6
x=3
3
1
= -3
11) log x
64
x-3 =
1
64
x3 = 64
3
x = 64
x=4
4
3x + 4
= 20
12) 4e
3x
+
4
e
=5
3x + 4 = ln(5)
3x = ln(5) - 4
ln(5) - 4
x=
3
x
- .797
- .797
3
Solve the equation. Give an exact solution.
13) ln(2x - 3) = ln (39 - 2x) - ln (x - 3)
39 - 2x
ln(2x - 3) = ln
x-3
(2x - 3) =
39 - 2x
x- 3
(2x - 3) x - 3 = 39 - 2x
2x 2 - 6x - 3x + 9 = 39 - 2x
2x 2 - 9x - 30 = - 2x
2x 2 - 7x - 30 = 0
2x + 5 x - 6 = 0
2x + 5 = 0
2x = - 5
5
x=2
x-6=0
x=6
6
Solve the equation. Round to four decimal places.
14) 75log 7(x) = 10
5
7log 7 (x ) = 10
x5 = 10
5
x = 10
x 1.5849
1.5849
Solve the equation. Give an exact solution.
15) log 4 (3x - 8) + log4 (3x + 8) = 2
log 4 (3x - 8)(3x + 8) = 2
42 = (3x - 8)(3x + 8)
16 = 9x 2 - 64
80 = 9x 2
80
= x2
9
x=±
80
3
x=±
4 5
3
4 5
3
4
Rewrite the expression as a single logarithm.
1
16) 4 logm x - 8 logm q2 - logm (r)
4
log m x 4 - log m q16 - log m (r1/4)
x4
log m
4
q16 r
Rewrite the expression as a sum or difference of logarithms or multiples of logarithms.
8
17) log 6
13c 2
log m x 4 - log m q16 - log m (r1/4)
x4
log m
4
q16 r
Use a calculator and the base-change formula to find the logarithm to four decimal places.
18) log 5 (93.38)
log 93.38
log 5
2.8188
5