Advanced Algebra 2: If, then worksheet
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Warm Up: Solve these three problems. Continue through the problem set (according to the prompts) until you have
completed 12 problems (including A, B, and C). This means you will end on either question 9, 12, or 15.
A.
log 3 ( 3x − 2 ) = 2
If you came up with these solutions ( x =
B.
1
log 3 x = 2 log 3 2
2
C.
9 x−1 = 27
11
5
, x = 16 , and x = ), then move on to the next set of directions.
3
2
Otherwise, rework the problem(s) or ask for help.
Start here: Solve each problem.
1.
log x + log ( x + 15 ) = 2
2.
3x = 14
3.
1
= 21−x
32
If you came up with these solutions ( x = 5 , x ≈ 2.402 , and x = 6 ) easily on your first attempt, then proceed to
questions 7-9. If you struggled a bit or had to redo some of them, then move on to questions 4-6.
4.
log ( x + 2 ) = log 7 + log x
If you came up with these solutions ( x =
5.
4 −1 = 8
3x
⎛ 1⎞
6. ⎜ ⎟
⎝ 6⎠
−3x−2
= 36 x+1
1
, x ≈ .5283 , and x = 0 ) easily on your first attempt, then move on to
3
questions 10-12. If you struggled a bit or had to redo some of them, then move on to questions 7-9.
7.
log 1 3 ( x 2 + x ) − log 1 3 ( x 2 − x ) = −1
8.
31−2 x = 4 x
9.
2 x ⋅ 4 x+5 = 4 2 x−1
If you came up with these solutions ( x = 2 , x ≈ .307 , and x = 12 ) fairly easily, then move on to questions 13-15. If
you struggled a bit or needed some hints, then move on to questions 10-12.
10.
ln x + ln ( x + 2 ) = 4
11.
π
1−x
=e
If you came up with these solutions ( x ≈ 6.43 , x ≈ .534 , and x =
13.
ln ( x + 1) − ln x = 2
14.
e x + e 3x
12. e ( e + e ) =
e− x
x
x
x
1
), then move on to questions 13-15.
3
250
= 200
1+ 4e−0.06 x
15.
If you came up with these solutions ( x ≈ .156 , x ≈ 46.2 , and x = 0 ), then you are done!
32 x + 3x+1 − 4 = 0