VCE Maths Methods Logs & Exponentials Mini Test 2
Number of marks: 8
Reading time: 2 minutes
Writing time: 12 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.
The expression \(\log_x(y) + \log_y(z)\), where \(x, y\) and \(z\) are all real numbers greater than 1, is equal to
- A. \(-\frac{1}{\log_y(x)} - \frac{1}{\log_z(y)}\)
- B. \(\frac{1}{\log_x(y)} + \frac{1}{\log_y(z)}\)
- C. \(-\frac{1}{\log_x(y)} - \frac{1}{\log_y(z)}\)
- D. \(\frac{1}{\log_y(x)} + \frac{1}{\log_z(y)}\)
- E. \(\log_y(x) + \log_z(y)\)
If \(y = a^{b-4x} + 2\), where \(a > 0\), then \(x\) is equal to
- A. \(\frac{1}{4}(b - \log_a(y-2))\)
- B. \(\frac{1}{4}(b - \log_a(y+2))\)
- C. \(b - \log_a(\frac{1}{4}(y+2))\)
- D. \(\frac{b}{4} - \log_a(y-2)\)
- E. \(\frac{1}{4}(b+2 - \log_a(y))\)
End of Section A
Section B – No Calculator
Instructions
• Answer all questions in the spaces provided.
• Write your responses in English.
• In questions where a numerical answer is required, an exact value must be given unless otherwise specified.
• In questions where more than one mark is available, appropriate working must be shown.
• Unless otherwise indicated, the diagrams in this book are not drawn to scale.
Solve \( e^{2x} - 12 = 4e^x \) for \( x \in \mathbb{R} \). 3 marks
Solve the equation \(2\log_2(x+5) - \log_2(x+9) = 1\). 3 marks
End of examination questions
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