Advanced Algebra 2: 25 Points Worksheet
Name__________________ Hour__
Complete problems of your choice so that the point value of this worksheet is 25 points. The point value for each
problem is listed by each problem. Additionally, you must complete at least one problem in each section.
Evaluate each expression without a calculator.
1.
log 1 16 (1 point)
3.
log 8 x =
5.
log 2 4 (1 point)
6.
log 3
8.
3log 3 5−log 3 4 (2 points)
9.
e
log 8 16 (1 point)
2.
4.
ln e8 (1 point)
7.
log 6 9 + log 6 4 (2 points)
2
1
(1 point)
9
log 2 16
e
1
(1 point)
3
(3 points)
Solve each equation.
10.
log 4 64 = x (2 points)
11.
log 2 ( 2x + 1) = 3 (2 points)
12.
log 6 36 = 5x + 3 (2 points)
13.
log 3 ( x 2 + 1) = 2 (3 points)
14.
e−2 x+1 = 13 (3 points)
15.
log 343 7 = x (2 points)
Write each expression as a single logarithm.
16.
3log 5 u + 4 log 5 v (1 point)
17.
log ( x 2 + 3x + 2 ) − 2 log ( x + 1) (1 point)
18.
21log 3 3 x + log 3 ( 9x 2 ) − log 3 9 (2 points)
19.
⎛ 4⎞
8 log 2 3x − 2 − log 2 ⎜ ⎟ + log 2 x (3 points)
⎝ x⎠
Write each expression as a sum or difference of logarithms. Express powers as factors.
20.
⎛ a⎞
log 2 ⎜ 2 ⎟ (1 point)
⎝b ⎠
⎛ x3 x + 1 ⎞
22. ln ⎜
(2 points)
2 ⎟
⎝ (x − 2) ⎠
21.
(
ln x 1+ x 2
)
⎛ (x − 4)2 ⎞
23. ln ⎜ 2
⎝ x − 1 ⎟⎠
(1 point)
2
3
(3 points)