| Exam Board | OCR |
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| Module | C2 (Core Mathematics 2) |
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| Year | 2009 |
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| Session | January |
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| Topic | Laws of Logarithms |
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8
- Given that \(\log _ { a } x = p\) and \(\log _ { a } y = q\), express the following in terms of \(p\) and \(q\).
- \(\log _ { a } ( x y )\)
- \(\log _ { a } \left( \frac { a ^ { 2 } x ^ { 3 } } { y } \right)\)
- Express \(\log _ { 10 } \left( x ^ { 2 } - 10 \right) - \log _ { 10 } x\) as a single logarithm.
- Hence solve the equation \(\log _ { 10 } \left( x ^ { 2 } - 10 \right) - \log _ { 10 } x = 2 \log _ { 10 } 3\).