Problem 1 :
The function h is given by h(x) = 8 ⋅ 2^{x}. For which of the following values of x, h(x) = 256?
A) x = 2
B) x = 5
C) x = 8
D) x = 16
Solution :
Problem 2 :
The function h is given by h(x) = log_{3 }x. Which of the following is equivalent to the expression
2 ⋅ h(w) + h(p),
where w and p are values in the domain of h?
A) log_{3} (wp)^{2}
B) (log_{3} w)^{2} ⋅ (log_{3} p)
C) log_{3} (w^{2}p)
D) log_{3} (2wp)
Solution :
Problem 3 :
Let x and y be positive constants. Which of the following is equivalent to 2ln x - 2 ln y ?
Solution :
Problem 4 :
The function f is given by f(x) = 2log_{5} x. Which of the following describes f?
A) is an increasing function that increases at an increasing rate.
B) is an increasing function that increases at a decreasing rate.
C) is a decreasing function that decreases at an increasing rate.
D) is a decreasing function that decreases at a decreasing rate.
Solution :
Problem 5 :
The Richter scale is a numerical scale that uses base 10 logarithms for measuring an earthquake’s magnitude. The larger the number, the more intense the earthquake. As intensities increase multiplicatively by a factor of 10, the Richter scale increases additively by 1. Consider two earthquakes that occurred in the year 2022. An earthquake in Indonesia had a magnitude of 5.1, and an earthquake in Mexico had a magnitude of 2.5. Approximately how many times more intense was the Indonesia earthquake than the Mexico earthquake?
A) 2.6
B) 26
C) 100
D) 400
Solution :
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