Edexcel AEA 2019 June — Question 1 7 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2019
SessionJune
Marks7
PaperDownload PDF ↗
TopicExponential Equations & Modelling
TypeLogarithmic equation solving
DifficultyStandard +0.8 Part (a) is a straightforward base conversion proof requiring only substitution and index laws. Part (b) requires applying the result from (a), then solving a quadratic equation with domain restrictions from logarithms. While this is multi-step and requires careful checking of validity, it's a standard logarithmic equation for AEA level without requiring novel insight—moderately above average difficulty.
Spec1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules

1.(a)By writing \(u = \log _ { 4 } r\) ,where \(r > 0\) ,show that $$\log _ { 4 } r = \frac { 1 } { 2 } \log _ { 2 } r$$ (b)Solve the equation $$\log _ { 4 } \left( 5 x ^ { 2 } - 11 \right) = \log _ { 2 } ( 3 x - 5 )$$

1.(a)By writing $u = \log _ { 4 } r$ ,where $r > 0$ ,show that

$$\log _ { 4 } r = \frac { 1 } { 2 } \log _ { 2 } r$$

(b)Solve the equation

$$\log _ { 4 } \left( 5 x ^ { 2 } - 11 \right) = \log _ { 2 } ( 3 x - 5 )$$

\hfill \mbox{\textit{Edexcel AEA 2019 Q1 [7]}}