帮我讲解一下这14道题---Question 1
Complete
Marked out of 1.00
Evaluate log₂8
(K:1)
a. 4
b. 5
c. 3
d. 2
Question 2
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Evaluate the approximate value of log₁₀50 (rounded to three decimal places).
(K:1)
a. 1.698
b. 1.045
c. 1.301
d. 1.699
Question 3
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Determine the exponential form equation that is equal to log₅25 = 2?
(K:1)
a. 5² = 125
b. 5² = 25
c. 2⁵ = 132
d. √25 = 5
Question 4
Complete
Marked out of 3.00
Identify which of the following expressions are equivalent to log₂8. Choose all that apply.
(K:3)
a. 3
b. log₂(16) - 1
c. log₂(4) + 1
d. log₂(2³)
Question 5
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Determine the x-intercept of the function, f(x) = log₃x
(I:1)
a. 0
b. 1
c. 3
Question 6
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Identify which of the following transformations is applied to y = log₂(x - 3).
(C:1)
a. Horizontal shift left by 3 units
b. Vertical stretch of 2
c. Horizontal shift right by 3 units
d. Vertical compression of 2
Question 7
Complete
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Solve for x.
log x = 2log5 + 3log4
(I:1)
a. 89
b. 1600
c. 120
d. 3.2
Question 8
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Determine the value of x for the equation 3²ˣ = 81.
(A:1)
a. x=3
b. x=1
c. x=4
d. x=2
Question 9
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Determine the value of x for the following equation: 3²ˣ⁺¹ = 81 × 27ˣ.
x = [Input Field]
(K:1)
Question 10
Complete
Marked out of 2.00
Identify which of the following are correct steps in solving for x in log₂(x + 3) = 5? Choose all that apply.
(A:2)
a. Exponentiate both sides with base 2.
b. Convert to base 10.
c. Subtract 3 from both sides.
d. Take the logarithm base 10 of both sides.
Question 11
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Determine the value of x for the equation log₃(x²-4)/(x-2) = 2
(K:1)
a. x=6
b. x=5
c. x=8
d. x=7
Question 12
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Which of the following functions results if f(x) = log₁₀x is vertically stretched by a factor of 4, horizontally stretched by a factor of 3, reflected in the y-axis, horizontally translated 5 units to the right and vertically translated 2 units up?
(I:1)
a. f(x) = 4log₁₀[-3(x - 5)] + 2
b. f(x) = 4log₁₀[-(x - 5)/3] + 2
c. f(x) = -4log₁₀[-(x - 5)/3] + 2
d. f(x) = -4log₁₀[-(x - 5)] + 2
Question 13
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A population of bacteria doubles every 3 hours. If the initial population is 500, determine how many bacteria there will be after 9 hours.
(A:1)
a. 4500
b. 1500
c. 4000
d. 256000
Question 14
Complete
Marked out of 1.00
Define the radian measure of an angle that subtends an arc length equal to the radius of the circle:
(K:1)
a. 1
b. 2π
c. π/2
d. π