Moderate -0.3 Part (i) is a straightforward logarithm equation requiring basic log laws and linear equation solving. Part (ii) involves applying the power law of logarithms and exponential form, which are standard C2 techniques. Both parts are routine applications with no problem-solving insight required, making this slightly easier than average for A-level.
7. (i) Find the exact value of \(x\) for which
$$\log _ { 2 } ( 2 x ) = \log _ { 2 } ( 5 x + 4 ) - 3$$
(ii) Given that
$$\log _ { a } y + 3 \log _ { a } 2 = 5$$
express \(y\) in terms of \(a\).
Give your answer in its simplest form.
7. (i) Find the exact value of $x$ for which
$$\log _ { 2 } ( 2 x ) = \log _ { 2 } ( 5 x + 4 ) - 3$$
(ii) Given that
$$\log _ { a } y + 3 \log _ { a } 2 = 5$$
express $y$ in terms of $a$.\\
Give your answer in its simplest form.\\
\hfill \mbox{\textit{Edexcel C2 2013 Q7 [7]}}