Solve \({\log _2}x + {\log _2}(x - 2) = 3\) , for \(x > 2\) .

recognizing \(\log a + \log b = \log ab\) (seen anywhere)     (A1)

e.g. \({\log _2}(x(x - 2))\) , \({x^2} - 2x\)

recognizing \({\log _a}b = x \Leftrightarrow {a^x} = b\)     (A1)

e.g. \({2^3} = 8\)

correct simplification     A1

e.g. \(x(x - 2) = {2^3}\) , \({x^2} - 2x - 8\)

evidence of correct approach to solve     (M1)

e.g. factorizing, quadratic formula

correct working     A1

e.g. \((x - 4)(x + 2)\) , \(\frac{{2 \pm \sqrt {36} }}{2}\)

\(x = 4\)     A2     N3

[7 marks]

Candidates secure in their understanding of logarithm properties usually had success with this problem, solving the resulting quadratic either by factoring or using the quadratic formula. The majority of successful candidates correctly rejected the solution that was not in the domain. A number of candidates, however, were unclear on logarithm properties. Some unsuccessful candidates were able to demonstrate understanding of one property but without both were not able to make much progress. A few candidates employed a “guess and check” strategy, but this did not earn full marks.