1. What is the value of $x$ that satisfies $\log_3(x + 2) + \log_3(x - 4) = 3$?
2. A worksheet asks you to simplify $\log(2)+\log(50)$ (base 10). Which single logarithm is equivalent?
3. A student wants a single logarithm equivalent to $\ln(12)-\ln(3)$. Which expression is equivalent?
4. What is $\log_{10}(1000)$?
5. Evaluate $\log_3(81)$.
6. A finance model uses natural logs. What is $\ln(e^5)$?
7. A calculator app uses base-10 logs. If $\log(x)= -2$, what is the value of $x$?
8. A student simplifies $\log_7(49)$. What is the value of $\log_7(49)$?
9. A student simplifies $\log_5(125)$. What is the value of $\log_5(125)$?
10. What is the value of $x$ if $\log(x) = 2$?
11. Convert $\log_{3}(27) = y$ into exponential form.
12. A measurement formula includes $\log(10^{-4})$ (base 10). What is its value?
13. $$\log_5(125)$ is equivalent to which of the following?
14. A student is rewriting a logarithmic equation in exponential form. Which equation is equivalent to $\log_{2}(32)=5$?
15. Which equation is equivalent to $\log_{10}(100) = 2$?
16. A student solves the equation $\ln(x)=0$. What is the value of $x$?
17. Which expression is equivalent to $\log(xy)$ using logarithm properties?
18. What is $\ln(e^2)$?
19. $$\log_7(49)$ equals what?
20. Solve for $x$ if $\log_3(x) = 4$.
21. If $\log_2(x) + \log_2(4) = 5$, what is the value of $x$?
22. Which equation is equivalent to $\log_6(36) = 2$?
23. What is the value of $n$ if $\log_4(64) = n$?
24. Convert $\log_{2}(16) = d$ to exponential form.
25. What is $\log_{4}(1)$?
26. Which expression is equivalent to $\log(\frac{x}{y})$?
27. $$\log_2(8)$ equals what?
28. What is $\log_{10}(0.01)$?
29. If $\log_5(25) = y$, what is $y$?
30. What is $\log_{10}(100)$?
31. Simplify the expression $\log_{10}(50)-\log_{10}(2)$.
32. What is the value of $\log_{10}(1000)$?
33. $$\log_2(8) + \log_2(4)$ equals what?
34. A student evaluates $\log_9(3)$. What is the value of $\log_9(3)$?
35. In simplifying a signal equation, you encounter $\ln\!\left(\dfrac{e^7}{e^2}\right)$. What is its value?
36. In a chemistry formula, you need $\log_4(\tfrac{1}{16})$. What is $\log_4\!\left(\dfrac{1}{16}\right)$?
37. A calculus student uses log rules to rewrite $\ln(\sqrt{e^{10}})$. What is its value?
38. A student is converting between logarithmic and exponential forms. Which equation is equivalent to $\log_3(81)=4$?
39. A student solves $\log(x)=2$ (base 10). What is the value of $x$?
40. Which equation is equivalent to $\log_5(1) = z$?
41. What is $\log_{e}(e^2)$?
42. Which equation is equivalent to $\log_3(9) = y$?
43. $$\log_2(16)$ is equivalent to which of the following?
44. Which expression is equivalent to $\log(10x)$?
45. For positive numbers $x$ and $y$, which expression is equivalent to $\log(xy)$ (base 10)?
46. In a chemistry calculation using natural logarithms, evaluate $\ln(e^5)$.
47. A sound engineer models intensity on a base-10 logarithmic scale. What is the value of $\log_{10}(1000)$?
48. A student solves a simple logarithmic equation. If $\log_{5}(x)=3$, what is $x$?
49. A researcher is simplifying a natural-log expression with positive values. Which expression is equivalent to $\ln\!\left(\dfrac{x}{y}\right)$?
50. For a positive constant $a$, simplify $\log_{10}(a^4)$ using the power rule.
51. A data analyst uses the fact that $\log(100)=2$ and $\log(10)=1$ (base 10). What is $\log(1000)$?
52. A scientist notes that $10^3 = 1000$. What is the value of $\log(1000)$ (base 10)?
53. To simplify an expression, you want to rewrite $\log(8^2)$ (base 10). Which expression is equivalent?
54. A student is told that logarithms require positive arguments. Which of the following expressions is <u>not</u> defined in the real numbers?
55. Solve for $x$ if $\ln(x) = 1$.
56. What is the result of $\log_5(1)$?
57. Convert $\log_{9}(81) = x$ to exponential form.
58. Evaluate $\log_{10}(0.01)$.
59. What is $\ln(1)$?
60. What is $\log(10^4)$?
61. $$\log_4(64)$ equals what?
62. Which expression is equivalent to $\ln(5x)$ for $x>0$?
63. If $\log_{10}(x)= -2$, what is the value of $x$?
64. Which equation is equivalent to $\log_{3}(81)=c$?
65. Evaluate $\log_{2}(32)$.
66. Solve for $x$: $\log_{4}(x)=\frac{1}{2}$.
67. A solution’s acidity is measured on the pH scale, where $\text{pH}=-\log_{10}(<u>H^+</u>)$. If $<u>H^+</u>=10^{-5}$, what is the pH?
68. Simplify $\log_{10}(x^{3})$ for $x>0$.
69. What is the value of $\ln(e^{7})$?
70. What is the result of $\log_{3}(27)$?
71. A student rewrites logarithms using properties. Which expression is equivalent to $\log\!\left(\dfrac{50}{2}\right)$ (base 10)?
72. Evaluate $\log_{5}(125)$.
73. In a calculation, you need to simplify $\log(4\cdot 25)$ (base 10). Which expression is equivalent?
74. A lab report states $\log_2(32)=x$. What is the value of $x$?
75. Which expression is equivalent to $\log(x^3)$?
76. $$\log_9(81)$ equals what?
77. What is the value of $k$ if $\log_3(27) = k$?
78. A physics student combines logarithms with the same base. If $\log_{3}(9)+\log_{3}(27)$ equals what single value?
79. If $\log_2(x) + \log_2(4) = 5$, what is the value of $x$?