Edexcel AEA 2017 Specimen — Question 6

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2017
SessionSpecimen
TopicLaws of Logarithms

6.(i)Eden,who is confused about the laws of logarithms,states that $$\left( \log _ { 5 } p \right) ^ { 2 } = \log _ { 5 } \left( p ^ { 2 } \right)$$ and \(\log _ { 5 } ( q - p ) = \log _ { 5 } q - \log _ { 5 } p\)
However,there is a value of \(p\) and a value of \(q\) for which both statements are correct.
Determine these values.
(ii)(a)Let \(r \in \mathbb { R } ^ { + } , r \neq 1\) .Prove that $$\log _ { r } A = \log _ { r ^ { 2 } } B \Rightarrow A ^ { 2 } = B$$ (b)Solve $$\log _ { 4 } \left( 3 x ^ { 3 } + 26 x ^ { 2 } + 40 x \right) = 2 + \log _ { 2 } ( x + 2 )$$
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