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)).

3 questions · Easy -1.2

Sort by: Default | Easiest first | Hardest first
OCR C2 Specimen Q3
7 marks Easy -1.2
3
  1. Express each of the following in terms of \(\log _ { 2 } x\) :
    1. \(\log _ { 2 } \left( x ^ { 2 } \right)\),
    2. \(\log _ { 2 } \left( 8 x ^ { 2 } \right)\).
  2. Given that \(y ^ { 2 } = 27\), find the value of \(\log _ { 3 } y\).
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 \(c\).
OCR MEI C2 2010 June Q7
2 marks Easy -1.2
7 Express \(\log _ { a } x ^ { 3 } + \log _ { a } \sqrt { x }\) in the form \(k \log _ { a } x\).