Moderate -0.3 Part (a) is routine application of log laws (power rule and combining logs). Part (b) requires taking logarithms of both sides and rearranging, which is standard A-level technique, though expressing the final answer in the specific form requires careful algebraic manipulation. Overall slightly easier than average due to being straightforward application of standard methods with no conceptual challenges.
9. a) Write the following as a single logarithm
$$3 \log ( x ) - \frac { 1 } { 2 } \log ( y ) + 2$$
b) Solve \(2 ^ { x } e ^ { 3 x + 1 } = 10\)
Giving your answer to (b) in the form \(\frac { \ln a + b } { \ln c + d }\), where \(a , b , c\) and \(d\) are integers. [0pt]
9. a) Write the following as a single logarithm
$$3 \log ( x ) - \frac { 1 } { 2 } \log ( y ) + 2$$
b) Solve $2 ^ { x } e ^ { 3 x + 1 } = 10$
Giving your answer to (b) in the form $\frac { \ln a + b } { \ln c + d }$, where $a , b , c$ and $d$ are integers.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q9 [5]}}