Redwood High School. Department of Mathematics
Avanced Algebra Test S2 #1 Frep worksheet
Hard worker's name:___________________________________
Solve the equation. If necessary, round to thousandths.
1) 2 (5x - 1) = 9
1)
2) 4 x = 17
2)
3) elnx = 17
3)
4)
1 x
=9
2
18) logb 49 =
2
3
1
= -3
19) log 5
125
Solve the equation.
20) 3 (1 + 2x) = 243
18)
19)
20)
4)
5) 3 (x - 1) = 10
6) 2e5x - 2 = 8
5)
6)
Find the exact value of the logarithmic expression.
1
7) log4
7)
64
8) log1/2 4
8)
9) log 9 1
21) 4 (x - 1) = 14
21)
1
22) 3 (6 + 3x) =
27
22)
23) 2 x = 16
23)
1
24) 4 (5 + 3x) =
256
24)
25)
9)
25) log 5 (x + 5) = 1 + log 5 (x
+ 2)
11
10)
26) log 3 x = 5
26)
11) log 10 1000
11)
27) log2 (3x - 2) - log2 (x - 5) =
4
27)
28) log 3 (2x + 7) = log 3 (2x
+ 4)
28)
29) 2 + log3 (2x + 5) - log3 x =
29)
10) log 11
Solve the equation. Give an exact solution.
12) log9 (x - 6) + log9 (x - 6) =
12)
1
13) log (x + 3) = 1 - log (x)
13)
14) ln(3x - 4) = ln(8) - ln(x - 2)
14)
15) ln(5x - 2) = ln(8) - ln(x - 4)
15)
4
Change the logarithmic expression to an equivalent
expression involving an exponent.
16) log 6 36 = x
16)
17) log 1/5 25 = -2
17)
1
1
30) 2 (5 - 3x) =
16
30)
31) 4 (3x - 1) = 11
31)
32) log (5 + x) - log (x - 5) =
log 3
32)
1 x
33) ( ) = 12
3
33)
Change the exponential expression to an equivalent
expression involving a logarithm.
34) 11x = 121
34)
1
35) 4 -2 =
16
35)
36) 163/4 = 8
36)
Express as a single logarithm.
1
37) (log5 (x - 4) - log5 x)
2
1
38) 5 log7 2 + log7 (x - 1) 4
37)
38)
1
log7 x
2
Rewrite the expression as a sum or difference of
logarithms or multiples of logarithms.
5
18
39) log19
39)
2
q p
40) logn
3 6x 3
z4
40)
41) log4
x7 y4
7
41)
Solve the problem.
42) The population in a
particular country is
growing at the rate of
2.2% per year. If 6,365,000
people lived there in 1999,
how many will there be in
the year 2004? Use
y = yoe0.022t and round
to the nearest
ten-thousand.
42)
2
43) At what interest rate must
$5200 be compounded
annually to equal $
10,229.19 after 10 yr?
(Round to the nearest
percent.)
43)
44) Find out how long it takes
a $3100 investment to
earn $300 interest if it is
invested at 7%
compounded monthly.
Round to the nearest
tenth of a year. Use the
r nt
formula A = P 1 +
.
n
44)
45) If Emery has $2000 to
invest at 8% per year
compounded monthly,
how long will it be before
he has $2400? If the
compounding is
continuous, how long will
it be? (Round your
answers to three decimal
places.)
45)
46) Larry has $1300 to invest
and needs $1900 in 13
years. What annual rate of
return will he need to get
in order to accomplish his
goal, if interest is
compounded
continuously? (Round
your answer to two
decimals.)
46)
47) ln (x - 5) - ln (x + 4) = ln
(x - 4) - ln (x + 8)
47)
Answer Key
Testname: ADVALG S2 TEST #1 LOGS PREP V2.0
1)
2)
3)
4)
5)
6)
7)
8)
9)
0.834
2.044
17
-3.170
3.096
0.677
-3
-2
0
1
10)
2
11) 3
12) 9
13) 2
10
14)
3
15)
22
5
16) 6 x = 36
1 -2
= 25
17)
5
18) b2/3= 49
1
19) 5 -3 =
125
20)
21)
22)
23)
24)
2
2.90
{-3}
4
-3
5
25) 4
26) {243}
27) {6}
28)
5
29)
7
30)
31)
32)
33)
34)
3
0.91
{10}
-2.26
log 11 121 = x
1
= -2
35) log 4
16
3
36) log 16 8 =
4
3
Answer Key
Testname: ADVALG S2 TEST #1 LOGS PREP V2.0
37) log5
38) log7
x-4
x
32
4
x-1
x
39)
1
log19 (18) - 2 log19 (q) - log19 (p)
5
40)
1
4
logn (6) + 1 logn (x) - logn (z)
3
3
41) 7 log4 (x) + 4 log4 (y) - log4 (7)
42)
43)
44)
45)
46)
47)
7,110,000
7%
1.3 years
2.287 yrs, 2.279 yrs
2.92%
8
4