Moderate -0.3 Part (i) requires straightforward application of logarithm laws (difference rule) and rearrangement to make b the subject. Part (ii) is a standard exponential equation solved by substitution (let y = 2^x), forming a quadratic, then taking logs. Both parts are routine C2 techniques with no novel insight required, making this slightly easier than average but not trivial due to the two-part structure and need for careful algebraic manipulation.
8. (i) Given that
$$\log _ { 3 } ( 3 b + 1 ) - \log _ { 3 } ( a - 2 ) = - 1 , \quad a > 2$$
express \(b\) in terms of \(a\).
(ii) Solve the equation
$$2 ^ { 2 x + 5 } - 7 \left( 2 ^ { x } \right) = 0$$
giving your answer to 2 decimal places.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
8. (i) Given that
$$\log _ { 3 } ( 3 b + 1 ) - \log _ { 3 } ( a - 2 ) = - 1 , \quad a > 2$$
express $b$ in terms of $a$.\\
(ii) Solve the equation
$$2 ^ { 2 x + 5 } - 7 \left( 2 ^ { x } \right) = 0$$
giving your answer to 2 decimal places.\\
(Solutions based entirely on graphical or numerical methods are not acceptable.)\\
\hfill \mbox{\textit{Edexcel C2 2016 Q8 [7]}}