Expand single log into combination

Express a single logarithm of a complex expression in terms of simpler logarithms (e.g., log_a(x²) = 2log_a(x), or log_a(x³√x) in terms of log_a(x)).

2 questions · Easy -1.5

1.06f Laws of logarithms: addition, subtraction, power rules
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OCR MEI C2 2007 January Q10
4 marks Easy -1.2
10
  1. Express \(\log _ { a } x ^ { 4 } + \log _ { a } \left( \frac { 1 } { x } \right)\) as a multiple of \(\log _ { a } x\).
  2. Given that \(\log _ { 10 } b + \log _ { 10 } c = 3\), find \(b\) in terms of \(c\).
AQA AS Paper 2 2023 June Q1
1 marks Easy -1.8
Simplify \(\log_a 8^a\) Circle your answer. [1 mark] \(a^3\) \qquad \(2a\) \qquad \(3a\) \qquad \(8a\)