Download Math 3 CHAPTER 4 TEST Name: Evaluate the exponential

Math 3
CHAPTER 4 TEST
Name:_______________________________________________
Evaluate the exponential expression.
1)
-3/4
- 16
-
1
163/4
1
- 3
2
-
2)
1
8
there are other ways to derive the correct answer but the symbols must also be correct.
12 - 2
-5
3
12 12 -
3-
-
3 5
2
243
32
243
8
729
= - 91.125
8
1
Graph the function. Use as many accurate points as possible. Find and identify the asymptote, domain and range of
the function. Show at least three transformations; as demonstrated in class. (10 points)
(x - 6)
1
+ 8 asymptote: y = 8
D: - ,
R: - , 8)
3) y = - · 2
4
Comnputer will not alloow me to grapn anymore points . You need to also have 9, 6 , 10, 4 , 11, 0 , 12, - 8
Find the value of the logarithmic function.
4) log 3 (729)
log 3 3 6
6
5)
ln e
-9
-9
2
6) log 1
1
256
log 1
1 4
4
4
4
4
Graph the function. Use as many accurate points as possible. Find and identify the asymptote, domain and range of
the function. Show at least three transformations; as demonstrated in class. (10 points)
7)
y = 5log1/3 (x + 12) - 4
asymptote: x = -12 D: - 12,
Write the equation as an equivalent logarithmic equation.
8)
z
x +4
=w
log z w = x + 4
Write the equation as an equivalent exponential equation.
9) log(m+ 3) = n
10n = m + 3
3
R: - ,
Rewrite the expression as a single logarithm.
1
10) log m 4 + 4 log m x - log m f - log m (r)
4
log m 4 + log m x 4 - log m f - log m (r1/4)
log m 4x 4 - logm f + logm (r1/4)
4
log m 4x 4 - logm (f r)
log m
4x 4
4
f r
Rewrite the expression as a sum or difference of logarithms or multiples of logarithms.
x 3
11) log 7
4c2
log 7 x 3 - log 7 4c2
log 7 x + log7
3 - log 7 4 + log 7 c2
log 7 x + log7 31/2 - log 7 4 - 2log7 c
log 7 x +
1
log7 3 - log 7 4 - 2log 7 c
2
Use a calculator and the base-change formula to find the logarithm to four decimal places.
12) log 1 3
5
log(3)
1
log 5
- .6826
4
Find the inverse of the function.
13)
x +2
f(x) = e
x +2
y=e
y+2
x= e
+3
+3
+3
y+2
x-3== e
ln x - 3 = y + 2
y = ln x - 3 - 2
f-1 x = ln x - 3 - 2
Solve the equation. Find the exact solution.
14) log 5 log2 log4 x = 0
log 2 log4 x
log 4 x = 2
=1
1
42 = x
x = 16
16
15) log 4 2x = log 4 24 - x 2
2x = 24 - x 2
x 2 + 2x - 24 = 0
x+6 x-4 =0
x=- 6
x=4
4
5
3
16) log x 27 =
4
x3/4 = 27
x = 27 4/3
x= 3 4
x = 81
81
17)
2434x = 9
3 5 4x = 3 2
320x = 3 2
20x = 2
x=
2
20
x=
1
10
1
10
18) log 5 (2x + 5) - log 5 (x + 5) = 1
log 5
51 =
2x + 5
=1
x+5
2x + 5
x+5
5(x + 5) = 2x + 5
5x + 25 = 2x + 5
3x = - 20
x=-
20
3
6
Solve the equation. If necessary, round to thousandths.
x+2
x
19) 6 = 3
log 6x = log 3
x+2
xlog(6) = (x + 2)log(3)
xlog(6) = xlog(3)+ 2log(3)
xlog(6) - xlog(3)= 2log(3)
x log(6) - log(3) = log(32)
xlog
6
3
= log(9)
xlog 2 = log(9)
x=
x
log(9)
log(2)
3.170
3.170
20)
e
x+5
x
= 20
x
x + 5 = ln 20
x + 5 =x ln 20
5 = x ln 20 - x
5 = x ln 20 - 1
x=
x
5
ln 20 - 1
2.505
2.505
7