# Math 2312 Precalculus Name ________________________________ Lab 2

```Math 2312 Precalculus
Lab 2
Professor Merrill
Name ________________________________
Show work and Circle answers
1. Solve: ln(x – 1) – ln(x + 1) = ln(x + 5)
Write each logarithmic equation in exponential form.
2. log3 81  4
3. log9 3 
1
2
Use properties of logarithms to condense
4. 3lnx+2lny
1
5. 2ln3-lnx+ ln y
3
Solve for x.
6. 5e x  7  32
7.
1 5x
e  8  13
3
8. How long does it take \$200 to double if invested at an 8% interest rate compounded
continuously?
Sketch two complete cycles of each graph. Draw and label axis. Label all critical points.
9.
3
y  12 cos 
4
10. y  3sin

4
(degrees)


11. y  6  sin  x 

2
12. y  1  cos  x   
Amp: _______
Period: _______
CI: ________
D: __________
Amp: _______
Period: _______
CI: ________
D: ___________
EP: ________
Range: _______
EP: ________
Range: _______
Amp: _______
Period: _______
CI: ________
D: ___________ Range: _____
Amp: _______
Period: _______
CI: ________ D: ___________
EP: ________
EP: ________
Range: _____
13. Give the period, amplitude and an equation for the graphs shown. Be sure to check your
answers by graphing on the calculator.
Period: _________Amplitude: _________
Equation:
______________________________
14. Determine period, amplitude, shifts, and equations for the graph shown.
P:__________ b:_________ A: ___________ VS:______________ PS:_____________
Sin Equation:_____________________________________________________________
Cos Equation:______________________________________________________________
Solve each of the following from
15.
2cos2 x  cosx  0
[0,2 ) . Give exact answers if possible.
16.
sin2 x  1 0
17.
2sin2 x  sinx  1  0
18.
19.
sinx  cscx
20.
tanx  2sinx
sin2 x  2cosx  2
21.
Let
u  AB and v  CD . Find the components of
each vector.
22.
Find the value of a if the vectors 2,5 and 1, a are orthogonal.
23.
Given A(4, 2) and B(0, -1). Give the component form of AB and find AB
24.
Find the angle between vectors U and V if U = (2,3) and V = (-3,2)
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