📚 Solving Equations Using Logarithms | 利用对数求解方程
At Edexcel A-level, equations where the unknown appears in an exponent are best handled by taking logarithms. This topic connects the index laws, the properties of logarithms, and domain restrictions, so it appears regularly in Pure Mathematics exam papers.
在 Edexcel A-level 考试中，未知数出现在指数上的方程最适合通过取对数来求解。本主题把指数律、对数性质和定义域限制联系起来，因此在 Pure Mathematics 试卷中经常出现。
1. Key Logarithm Rules | 对数核心法则
Before solving equations, make sure you can apply the three main laws of logarithms in both directions. They are valid for any base a > 0 and a ≠ 1, with x > 0 and y > 0.
在解方程之前，确保你能双向使用三条主要对数法则。这些法则对任意底数 a > 0 且 a ≠ 1 成立，同时要求 x > 0、y > 0。
| Product rule | logₐ(xy) = logₐ x + logₐ y |
| Quotient rule | logₐ(x/y) = logₐ x – logₐ y |
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