| Exam Board | Edexcel |
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| Module | AS Paper 1 (AS Paper 1) |
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| Year | 2022 |
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| Session | June |
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| Topic | Laws of Logarithms |
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- (a) Given that \(p = \log _ { 3 } x\), where \(x > 0\), find in simplest form in terms of \(p\),
- \(\log _ { 3 } \left( \frac { x } { 9 } \right)\)
- \(\log _ { 3 } ( \sqrt { x } )\)
(b) Hence, or otherwise, solve
$$2 \log _ { 3 } \left( \frac { x } { 9 } \right) + 3 \log _ { 3 } ( \sqrt { x } ) = - 11$$
giving your answer as a simplified fraction.
Solutions relying on calculator technology are not acceptable.