State value of basic log

1 Candidates answer on the Question Paper.
Additional Materials: List of Formulae (MF9) \section*{READ THESE INSTRUCTIONS FIRST} Write your Centre number, candidate number and name in the spaces at the top of this page.
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[0pt] The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50. This document consists of 11 printed pages and 1 blank page. 1 Solve the equation \(\ln ( 3 x + 1 ) - \ln ( x + 2 ) = 1\), giving your answer in terms of e.

5

1. Write down the value of \(\log _ { 5 } 5\).
2. Find \(\log _ { 3 } \left( \frac { 1 } { 9 } \right)\).
3. Express \(\log _ { a } x + \log _ { a } \left( x ^ { 5 } \right)\) as a multiple of \(\log _ { a } x\).

9

1. State the value of \(\log _ { a } a\).
2. Express each of the following in terms of \(\log _ { a } x\).
   (A) \(\log _ { a } x ^ { 3 } + \log _ { a } \sqrt { x }\) (B) \(\log _ { a } \frac { 1 } { x }\) Section B (36 marks)

4 Given that \(a > 0\), state the values of

1. \(\log _ { a } 1\),
2. \(\log _ { a } \left( a ^ { 3 } \right) ^ { 6 }\),
3. \(\log _ { a } \sqrt { a }\).

1 It is given that \(8 ^ { 4 x } = 4 ^ { 3 x - 6 }\).

1. By expressing each side as a power of 2 , find the value of \(x\).
2. Write down the value of \(\log _ { 4 } | x |\).

Write down the values of \(\log_a a\) and \(\log_a (a^3)\). [2]

Write down the value of (A) \(\log_a (a^4)\), [1] (B) \(\log_a \left(\frac{1}{a}\right)\). [1]