Redwood High School. Department of Mathematics
Hard worker's name:___________________________________
2015-2016 H Advanced Algebra prep worksheet #1 for Test S2 #4. SHOW YOUR WORK
Express as a single logarithm.
1) log x + log (x2 - 225) - log
7 - log (x - 15)
13) log 4 (x + 5) + log 4 (x - 1)
=2
1)
1
16
14)
2
15) 2 x - 3= 64
15)
14) 2 5 - 3x =
Solve the logarithmic equation. Be sure to reject any value
that is not in the domain of the original logarithmic
expressions. Give the exact answer.
2) 2log x - log 4 = log 169
2)
13)
3) log3 (x - 2) - log3 (x - 3)
=4
3)
16) log3 (x2 - 2x) = 1
16)
4) log (x + 24) - log 3 = log (
4x + 1)
4)
17) log 21 (x + 84) = 3 log 21 x
17)
18) How long must $5200 be
in a bank at 7%
compounded annually to
become $10,229.19?
(Round to the nearest
year.)
18)
Solve the equation. If necessary, round to thousandths.
5) 4e5x - 3 = 24
5)
6) 5 (2x - 3) = 17
6)
7) log2 (3x - 2) - log2 (x - 5) =
4
7)
Solve the equation.
19) 4 x - 1 = 8 2x
Solve the equation. Give an exact solution.
8) log (x - 9) = 1 - log (x)
8)
9) log4 (x - 2) + log4 (x - 2) =
1
10) 2 (7 - 3x) =
1
4
9)
10)
19)
20) log 2 (x + 3) + log 2 (x - 3)
=4
20)
21) log5 (x2 - 4x) = 1
21)
22) log3 (x + 5) - log3 (x + 2)
22)
=2
Solve the problem.
11) An initial investment of
$12,000 is appreciated for
2 years in an account that
earns 12% interest,
compounded quarterly.
Find the amount of
money in the account at
the end of the period.
12) log2 (3x - 2) - log2 (x - 5) =
23) 3 (3x - 6 ) = 27
11)
23)
Write as the sum and/or difference of logarithms. Express
powers as factors.
(x + 3)(x - 8) 2/5
,
x 24)
24) ln
(x - 7)4
>8
12)
4
1
Answer Key
Testname: ADVALG S2 TEST #4 LOGS WKSV1.0
1) log
x(x + 15)
7
2) {26}
241
}
3) {
80
4)
21
11
5) 0.958
6) 2.380
7) {6}
8) 10
9) 4
10) 3
11) $15,201.24
12) {6}
13) {3}
14) {3}
15) {3, -3}
16) {3, -1}
17) {63}
18) 10 yr
1
19) 2
20) {5}
21) {5, -1}
13
22) {- }
8
23) {3}
2
2
8
24) ln (x + 3) + ln (x - 8) - ln (x - 7)
5
5
5
2