Moderate -0.3 This is a straightforward algebraic manipulation question requiring substitution (let y = 2^(3x)), solving a linear equation, then applying logarithms. While it involves multiple steps, each step is routine and the substitution strategy is clearly signposted by the question structure. Slightly easier than average due to the guided approach and standard techniques.
2 Given that \(\frac { 2 ^ { 3 x + 2 } + 8 } { 2 ^ { 3 x } - 7 } = 5\), find the value of \(2 ^ { 3 x }\) and hence, using logarithms, find the value of \(x\) correct to 4 significant figures.
2 Given that $\frac { 2 ^ { 3 x + 2 } + 8 } { 2 ^ { 3 x } - 7 } = 5$, find the value of $2 ^ { 3 x }$ and hence, using logarithms, find the value of $x$ correct to 4 significant figures.\\
\hfill \mbox{\textit{CAIE P2 2020 Q2 [5]}}