AP Precalculus -2.9 Logarithmic Expressions- MCQ Exam Style Questions - Effective Fall 2023

AP Precalculus -2.9 Logarithmic Expressions- MCQ Exam Style Questions – Effective Fall 2023

AP Precalculus -2.9 Logarithmic Expressions- MCQ Exam Style Questions – AP Precalculus- per latest AP Precalculus Syllabus.

The function \( h \) is given by \( h(x) = 5 \cdot 3^{(-x/2)} \). What is the value of \( h(1) \)?

(A) \( -5\sqrt{3} \)
(B) \( \frac{1}{\sqrt{15}} \)
(C) \( \frac{5}{9} \)
(D) \( \frac{5}{\sqrt{3}} \)

▶️ Answer/Explanation

Detailed solution

\( h(1) = 5 \cdot 3^{(-1/2)} = 5 \cdot \frac{1}{3^{1/2}} = \frac{5}{\sqrt{3}} \).
✅ Answer: (D)

The function \(f\) is given by \(f(x)=\log_{2}x\). What input value in the domain of \(f\) yields an output value of \(4\)?

(A) \(32\)
(B) \(16\)
(C) \(2\)
(D) \(\frac{1}{2}\)

▶️ Answer/Explanation

Detailed solution

1. Set up the equation:
Set \(f(x) = 4\):
\(\log_{2}x = 4\)

2. Convert to exponential form:
\(x = 2^4\)

3. Calculate:
\(x = 16\)

✅ Answer: (B)