Description
Do all the questions in tests 7&8 (attached)
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Explanation & Answer
These answers are double checked.
TEST 7
1. I need the parts of this question.
This graph increases rapidly, always positive and has 1 at 𝑥 = 0.
5 𝑥
𝟔 −𝒙
2. 𝑦 = (6) = (𝟓) .
3. 𝑆(4) = 2000(1.02)16 ≈ 𝟐𝟕𝟒𝟓. 𝟓𝟕.
4. 𝑆(0) = 𝑃 = 1000, 𝑆(20) = 1000𝑒 1 ≈ 2700, so the upper right graph.
𝟏
3
5. log 3 (𝑥 √𝑥 + 8) = 𝐥𝐨𝐠 𝟑 (𝒙) + 𝟑 𝐥𝐨𝐠 𝟑 (𝒙 + 𝟖).
𝟑𝒙
6. ln(3𝑥) − ln(3𝑦) = 𝐥𝐧 (𝟑𝒚).
1
7. log 5 (𝑥 + 6) + log 5 (𝑥) = 𝐥𝐨𝐠 𝟓 ((𝒙 + 𝟔)√𝒙).
2
8. (a) log 6 17 =
ln 17
ln 6
≈ 𝟏. 𝟓𝟖𝟏𝟐. (b) log 3 0.52 =
ln 0.52
ln 3
≈ −𝟎. 𝟓𝟗𝟓𝟐.
𝐥𝐧 𝒙
9. 𝑦 = log 3 𝑥 = 𝐥𝐧 𝟑, this function increases and has zero at 𝑥 = 1, so the upper right
graph.
𝐼
10. 𝐿 = 10 log (𝐼 ) = 10 log 10000 = 10 log10 104 = 𝟒𝟎.
0
11.
(a) − log(3.98 ∙ 10−8 ) = 8 log(3.98) ≈ 𝟒. 𝟖.
(b) − log(6.31 ∙ 10−5 ) = 5 log(6.31) ≈ 𝟒. 𝟎.
(c) − log(6.30 ∙ 10−3 ) = 3 log(6.30) ≈ 𝟐. 𝟒.
12. 9(6𝑥) = 4782969, ln: ln 9 ∙ 6𝑥 = ln(4782969) , 𝑥 =
ln(4782969)
6 ln 9
7
= 6 ≈ 1.1666.
100−79
13. 79 = 100 − 100𝑒 −0.04𝑥 , 𝑒 −0.04𝑥 = 100 = 0.21, ln: − 0.04𝑥 = ln(0.21),
− ln(0.21)
𝑥=
≈ 𝟑𝟗. 𝟎𝟏𝟔.
0.04
14. log 4 (9𝑥 + 10) = 3. Apply 4𝑦 to both parts and get 9𝑥 + 10 = 43 = 64,
so 9𝑥 = 54, 𝒙 = 𝟔.
𝑥
15. ...