| Exam Board | CAIE |
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| Module | P3 (Pure Mathematics 3) |
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| Year | 2024 |
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| Session | March |
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| Topic | Laws of Logarithms |
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4 The positive numbers \(p\) and \(q\) are such that
$$\ln \left( \frac { p } { q } \right) = a \text { and } \ln \left( q ^ { 2 } p \right) = b .$$
Express \(\ln \left( p ^ { 7 } q \right)\) in terms of \(a\) and \(b\).