Homework 5*****Already A++ Rated Tutorial*****Use as Guide Paper*****
Smart Study1. Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents.
31-x = 1/27
A. {2} | ||
B. {-7} | ||
C. {4} | ||
D. {3} | ||
2.5 Points | ||
2. Perform the long division and write the partial fraction decomposition of the remainder term.
x4 – x2 + 2/x3 - x2
A. x + 3 - 2/x - 1/x2 + 4x - 1 | ||
B. 2x + 1 - 2/x - 2/x + 2/x + 1 | ||
C. 2x + 1 - 2/x2 - 2/x + 5/x - 1 | ||
D. x + 1 - 2/x - 2/x2 + 2/x - 1 | ||
2.5 Points | ||
3. Solve each equation by either substitution or addition method.
x2 + 4y2 = 20 |
A. {(5, 2), (-4, 1)} | |
B. {(4, 2), (3, 1)} | |
C. {(2, 2), (4, 1)} | |
D. {(6, 2), (7, 1)} |
2.5 Points |
4. Solve the following system by the addition method.
{2x + 3y = 6
{2x – 3y = 6
A. {(4, 1)} | ||
B. {(5, 0)} | ||
C. {(2, 1)} | ||
D. {(3, 0)} | ||
| 0.0/ 2.5 Points | |
5. Find the domain of following logarithmic function.
f(x) = ln (x - 2)2
A. (∞, 2) ∪ (-2, -∞) | ||
B. (-∞, 2) ∪ (2, ∞) | ||
C. (-∞, 1) ∪ (3, ∞) | ||
D. (2, -∞) ∪ (2, ∞) | ||
0.0/ 2.5 Points | ||
6. Find the domain of following logarithmic function.
f(x) = log (2 - x)
A. (∞, 4) | ||
B. (∞, -12) | ||
C. (-∞, 2) | ||
D. (-∞, -3) | ||
0.0/ 2.5 Points | ||
7. Perform the long division and write the partial fraction decomposition of the remainder term.
x5 + 2/x2 - 1
A. x2 + x - 1/2(x + 1) + 4/2(x - 1) |
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B. x3 + x - 1/2(x + 1) + 3/2(x - 1) | ||
C. x3 + x - 1/6(x - 2) + 3/2(x + 1) | ||
D. x2 + x - 1/2(x + 1) + 4/2(x - 1) |
8. Solve each equation by the substitution method.
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9. Write the partial fraction decomposition for the following rational expression.
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10. Write the partial fraction decomposition for the following rational expression.
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0.0/ 2.5 Points |
11. Write the form of the partial fraction decomposition of the rational expression.
5x2 - 6x + 7/(x - 1)(x2 + 1)
A. A/x - 2 + Bx2 + C/x2 + 3 | |
B. A/x - 4 + Bx + C/x2 + 1 | |
C. A/x - 3 + Bx + C/x2 + 1 | |
D. A/x - 1 + Bx + C/x2 + 1 |
12. Solve the following system.
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0.0/ 2.5 Points |
13. Write the partial fraction decomposition for the following rational expression.
4/2x2 - 5x – 3
A. 4/6(x - 2) - 8/7(4x + 1) | |
B. 4/7(x - 3) - 8/7(2x + 1) | |
C. 4/7(x - 2) - 8/7(3x + 1) | |
D. 4/6(x - 2) - 8/7(3x + 1) |
14. Use properties of logarithms to expand the following logarithmic expression as much as possible.
Logb (√xy3 / z3)
A. 1/2 logbx - 6 logby + 3 logbz | |
B. 1/2 logb x - 9 logb y - 3 logb z | |
C. 1/2 logb x + 3 logb y + 6 logb z | |
D. 1/2 logb x + 3 logb y - 3 logb z |
2.5 Points |
15. Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.
3 ln x – 1/3 ln y
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