Question 9 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2015
Session	June
Marks	5
Topic	Exponential Equations & Modelling

Use logarithms to solve the equation $2 ^ { 3 x } = 5$, giving your value of $x$ to three significant figures.
Given that $\log _ { a } k - \log _ { a } 2 = \frac { 2 } { 3 }$, express $a$ in terms of $k$.
1. By using the binomial expansion, or otherwise, express $( 1 + 2 x ) ^ { 3 }$ in ascending powers of $x$.
2. It is given that $$\log _ { 2 } \left[ ( 1 + 2 n ) ^ { 3 } - 8 n \right] = \log _ { 2 } ( 1 + 2 n ) + \log _ { 2 } \left[ 4 \left( 1 + n ^ { 2 } \right) \right]$$ By forming and solving a suitable quadratic equation, find the possible values of $n$. [5 marks] \includegraphics[max width=\textwidth, alt={}, center]{24641e66-b73b-4323-98c8-349727151aba-20_1581_1714_1126_153}
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