VCE Maths Methods Logs & Exponentials Mini Test 4
Number of marks: 10
Reading time: 2 minutes
Writing time: 15 minutes
Section A – Calculator Allowed
Instructions
• Answer all questions in pencil on your Multiple-Choice Answer Sheet.
• Choose the response that is correct for the question.
• A correct answer scores 1; an incorrect answer scores 0.
• Marks will not be deducted for incorrect answers.
• No marks will be given if more than one answer is completed for any question.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Let \(f: R^+ \to R, f(x) = k\log_2(x), k \in R\).
Given that \(f^{-1}(1) = 8\), the value of \(k\) is
- A. \(0\)
- B. \(\frac{1}{3}\)
- C. \(3\)
- D. \(8\)
- E. \(12\)
End of Section A
a. Solve \( 10^{3x - 13} = 100 \) for \( x \). 2 marks
b. Find the maximal domain of \( f \), where \( f(x) = \log_e(x^2 - 2x - 3) \). 3 marks
Solve \( 2\log_3(x - 4) + \log_3(x) = 2 \) for \( x \). 4 marks
End of examination questions
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