Download Math 45 Sample Test # 4

College-Algebra, Take Home Test 4
Chapter 5.2 - 5.6 & 7.1 - 7.3: Exponential & Logarithmic Functions, Analytic Geometry
(Conic Sections)
Name_______________________
Print, solve all problems completely, and bring it on the day of the 4th on campus exam for full credit.
1. Find x:
(a) log2 x = 54 …nd x.
b) log2 32 = x
c) logx 121 = 2
d) 2x = 8
2. Simplify:
(a) Find ln e100
c) log4 45
b) log125 5
d)7 log9 81
3. Find x:
(a) log2 log7 49 = x
b) Find log1=5 x =
c) 22x+3 = 32
2
4. Write each exponential form in logarithmic form.
(a) 53 = 125
b) (1=8)
2
c) ab = c
= 64
5. Write each logarithmic form in exponential form.
(a) log2 64 = 6
______________b) ln m = n
2
_______________
_______________c) log 0:01 =
6. Use the properties of the logs to rewrite each expression as a single logarithm with coe¢ cient 1.
(a) 100 log (2x + 31) + 5 log (x
1)
3 log(z + 5)
1
logb (x + z + z)
3
(b) logb (x + y)
7. Use the properties of the logs to decompose the following to logarithms of …rst degree polynomials.
(a) ln p
3
ex5
x3 1
b) log
10x (x + 10)
(25
2
5
x)
8. Graph the following functions.by starting with the graph of the functions f (x) = ex , and f (x) = ln x:
Indicate the domain, Range, x and y intercept and the asymptote.
(a) y = ex+1
3
9. Given x = 5k ln(kz
10. Given A = T0 + Ce
b) f (x) = ln(x
1) solve for z:
kt
solve for k:
11. Solve:
1
1)
162
=x
2 3
(b) log x + log (3x 13) = 1
(a) log1=4
c) log5 (x + 2) + log5 (x
d) ln (x + 5) + ln (x
12. Find the exact solution, and an approximation to 4 decimals:.
2
1)
2) = 1
ln 7 = 0
32x = 7x
1
13. Solve.
(a) 274x = 9x+1
(b)
3
5
2x 1
=
1
64
(c) logx
(d) e3x
4
=
25
9
x
1
6
=1
14. Assume logb 2 = A; logb 3 = B; and logb 5 = C: evaluate
15. Find the domain of the function: f (x) = log x2
logb
p
25
:
36
1
16. For an investment of $1000 to grow to $1400 in 5 years. use A = P 1 +
r
n
nt
:
(a) What rate of interest, compounded monthly is needed?
(b) Find the doubling time to 4 decimal places.
17. The amount of carbon-14 after t years is given by the exponential equation A(t) = A0 e
ln 2
k=
5730
(a) Find the half life.
(b) A bone contains 15% of the normal amount of carbon -14. Estimate,the age of the bone.
18. The population of a town after t years is given by P (t) = 5000e0:2t
(a) What is the initial population?
(b) When will the population double?
(c) When will the population grow to 8000?
19. Find the coordinates of the center, and the radius of the graph of the equation :
(a) x2 + y 2
2
4x + 2y
31 = 0
2
(b) x + y + 3x + 12y + 50 = 0
(c) x2 + y 2 + 2x
6y + 10 = 0
20. Identify the graph of the equation.:
(a) 4x2 + 9y 2
36 = 0
b) 10x2 + 10y 2 = 90
21. Write the equation of the circle. and graph:
c) x2
3y 2 = 10
Center(3; 4) ;radius 4:
3
kt
;with
22. Find the vertex, focus, and directrix of the parabola y = 3x2 +12x+8; indicate which way the parabola
opens and sketch the graph.
2
23. Graph the ellipse
2
(x + 1)
(y 5)
+
= 1; by …nding its center, foci, and vertices and the ecentricity.
36
9
24. Graph the Hyperbola using a and b: Find the asymptotes and the ecentricity:
4
x2
16
y2
=1
9