C) 18
D) 4.5
17. Solve for \(x\): \(\sqrt[3]{x - 2} = 4\).
A) 6
B) 14
C) 66
D) 64
18. Simplify \(\sqrt{75}\).
A) \(5\sqrt{3}\)
B) \(3\sqrt{5}\)
C) \(25\sqrt{3}\)
D) \(5\sqrt{5}\)
19. Solve \(\sqrt{2x + 5} = 5\).
A) 10
B) 15
C) 0
D) 25
20. Solve \(x^{3/2} = 8\).
A) 4
B) 16
C) 64
D) 2
21. Simplify \(\sqrt{x} \cdot \sqrt[3]{x}\).
A) \(x^{1/6}\)
B) \(x^{5/6}\)
C) \(\sqrt[5]{x}\)
D) \(x^{2/3}\)
22. Solve \(\sqrt{x + 2} = x\).
A) \(x = 2, -1\)
B) \(x = 2\)
C) \(x = -1\)
D) No solution
23. Simplify \((x^{1/2}y^{1/3})^6\).
A) \(xy\)
B) \(x^3y^2\)
C) \(x^{12}y^{18}\)
D) \(x^6y^6\)
24. Simplify \(\sqrt[4]{81x^{12}}\).
A) \(9x^3\)
B) \(3x^3\)
C) \(3x^4\)
D) \(27x^3\)
25. Evaluate \(27^{-2/3}\).
A) \(1/9\)
B) -9
C) 9
D) \(-1/9\)
Part 2: Logarithms & Exponentials
26. Evaluate \(\log_2 8\).
A) 2
B) 3
C) 4
D) 64
27. Evaluate \(\log_6 \frac{1}{36}\).
A) -2
B) 2
C) -6
D) \(1/2\)
28. Expand \(\log_8 3xy\).
A) \(\log_8 3 + \log_8 x + \log_8 y\)
B) \(\log_8(3 + x + y)\)
C) \(\log_8 3 \cdot \log_8 x \cdot \log_8 y\)
29. Expand \(\ln \frac{12x^5}{y}\).
A) \(\ln 12 + 5 \ln x - \ln y\)
B) \(5 \ln 12 + \ln x - \ln y\)
C) \(\ln 12 - 5 \ln x - \ln y\)
30. Condense \(3\log_7 4 + \log_7 6\).
A) \(\log_7 18\)
B) \(\log_7 72\)
C) \(\log_7 192\)
D) \(\log_7 384\)
31. \(\log_2 10\) (to 3 decimals).
A) 0.301
B) 3.322
C) 5.000
D) 0.200
32. Value of \(\log_{23} 42\) (CoB)?
A) \(\frac{\log 23}{\log 42}\)
B) \(\frac{\ln 42}{\ln 23}\)
C) \(\log 42 - \log 23\)
33. Inverse of \(f(x) = 8^x\).
A) \(f^{-1}(x) = \log_x 8\)
B) \(f^{-1}(x) = x^8\)
C) \(f^{-1}(x) = \log_8 x\)
D) \(f^{-1}(x) = 1/8^x\)
34. Evaluate \(\log_3 8 + \log_3 \frac{1}{2}\).
A) \(\log_3 4\)
B) \(\log_3 8.5\)
C) \(\log_3 16\)
D) 4
35. \(\log_3 4 \approx 1.262\), \(\log_3 13 \approx 2.335\). \(\log_3 52\)?
A) 1.073
B) 2.947
C) 3.597
D) 4.859
36. \((\frac{1}{3})^x\) to \((\frac{1}{3})^{x-1} + 3\).
A) Translation 1 right, 3 up
B) Translation 1 left, 3 down
C) Translation 1 right, 3 down
37. \(e^{-x}\) to \(e^{-5x} - 8\).
A) Horizontal shrink by 1/5, 8 down
B) Vertical stretch by 5, 8 down
C) Reflection in x-axis, 8 down
38. Asymptote of \(y = 4e^{-2x} + 5\)?
A) \(y = 0\)
B) \(y = 4\)
C) \(y = 5\)
D) \(x = -2\)
39. Domain/Range of \(y = \log_{1/5} x\).
A) Domain: \(x > 0\); Range: all real
B) Domain: all real; Range: \(y > 0\)
C) Domain: \(x < 0\); Range: all real
40. Inverse of \(y = \ln(x - 4)\).
A) \(y = e^x - 4\)
B) \(y = e^x + 4\)
C) \(y = \ln(x+4)\)
D) \(y = e^{x-4}\)
41. Shrink factor of \(\frac{1}{2}\log_4(x+5)\)?
A) 4
B) 5
C) \(1/2\)
D) 2
42. Passes through (0,1), (1,4). Growth \(b\)?
A) 1
B) 4
C) 0
D) 5
43. Translation of \(\log x\) 9 units right?
A) \(y = \log(x + 9)\)
B) \(y = \log(x - 9)\)
C) \(y = \log x + 9\)
D) \(y = \log x - 9\)
44. Solve the equation: \(5^x = 8\).
A) 0.625
B) 1.292
C) 1.600
D) 1.386
45. Solve: \(\ln(3x - 9) = \ln(2x + 6)\).
A) \(x = 3\)
B) \(x = 15\)
C) \(x = -3\)
D) \(x = 1.5\)
46. Solve: \(\log_3(2x - 5) = 2\).
A) \(x = 3.5\)
B) \(x = 4.5\)
C) \(x = 7\)
D) \(x = 14\)
47. \(y = ab^x\) through (1, 3) and (4, 24).
A) \(y = 3(2^x)\)
B) \(y = 1.5(2^x)\)
C) \(y = 2(1.5^x)\)
48. \(y = 12.263 \ln x - 45.381\). For \(x = 1000\).
A) 39.3
B) 84.7
C) 12.3
D) 129.5
49. \(y = 4200(0.9)^x\) after 2 years.
A) $3402
B) $3780
C) $3062
D) $2755
50. Why check extraneous solutions?
A) Logs defined only for positive numbers.
B) The base of a logarithm cannot be 1.
C) Exponential functions never reach zero.
End of Assessment
