Algebraic Thinking, Week 9 Tools quiz, logs and trig Name _______________________________________
1. Sketch a quick graph of log x using x values of x=.1, x=1, and x=10
3 points would be: (.1, -1) (1,0) and (10,2).. connect
2. 100101 (base 2) = ____________ (base 10)
37
3. Estimate log (base 3) of 75 (within a couple of tenths) Explain your answer
About 3.9. 3^3 = 27 3^4 = 81… close to, but a little less than 4
4. Express log (base 5) 55.9 = 2.5 in exponential format
5^(2.5) = 55.9
5. Express 10^.3 = 2 in log format.
Log(2) = .3
6. Rewrite using the product rule: log (6x)
Log(2) + log(3) + log(x)
7. Rewrite as a single log: ( log(x) + log(3) ) – log(2)
Log(3x/2)
8. Solve for t using the log power rule. Show your work: 10^t = 35
Log(10^t) = log(35) or t log(10) = log(35) or t = log(35) / log(10)
9. How long before $15000 invested at 5 percent will get to $50,000?
A = Pr^t or 50000 = 15000(1.05)^t or 50000/15000 = (1.05)^t or log(3.33) = log(1.05^t) or
log(3.33) = t log(1.05) or log(3.33) / log(1.05) = t or t = about 25 years
Problems 10 uses the similar triangle pair on the board.
10. If side A is 7, corresponding side x is 2, and side y is 3, what is side B?
B = 10.5
11. Given the above distances, if side C = 21, what is side z?
Z = 6
In problems 12-15, Use the right triangle on the board with sides DEF and angle a The adjacent side of angle a is D, the opposite side of angle a is E and the hypotenuse of the right triangle is F
12. What is the sin a?
E/F
13. What is the tan a?
E/D
14. What is the adjacent side of angle a?
Side D
15. If D = 12 and E = 5, what is the measure of angle a?
Tan(a) = E/D or tan(a) = 5/12 or tan(a) = .416 or angle a = 22.5 degrees
16. If angle a is 15 degrees, and side E is 12, find side F
Sin(15) = 12/F or .258 = 12/F or F = 46.5
17. If angle a is 25 degrees, side D is 9, find side E
Tan(25) = E/9 or .466 = E/9 or E = 4.2