IB Mathematics: Exponents and Logarithms Operations | IB数学：指数与对数运算全解析

📚 IB Mathematics: Exponents and Logarithms Operations | IB数学：指数与对数运算全解析

Exponents and logarithms are two sides of the same coin. In IB Mathematics, you must be able to switch fluently between exponential and logarithmic forms, apply the laws correctly, and solve equations in a variety of contexts.

指数与对数就像同一枚硬币的两面。在 IB 数学中，你必须能够在指数形式与对数形式之间灵活转换，正确运用运算法则，并在多种情境中求解方程。

1. Exponent Rules | 指数法则

The exponent rules are derived from repeated multiplication. They are valid for positive bases and real exponents, with the usual restrictions for non-integer exponents.

指数法则源自于重复乘法的定义。它们对正底数和实数指数均成立，但在非整数指数时需注意通常的限制。

• Product rule: a^m × aⁿ = a^m+n

  乘积法则：a^m × aⁿ = a^m+n

• Quotient rule: a^m ÷ aⁿ = a^m−n

  商法则：a^m ÷ aⁿ = a^m−n

• Power of a power: (a^m)ⁿ = a^m·n

  幂的乘方：(a^m)ⁿ = a^m·n

• Power of a product: (ab)ⁿ = aⁿbⁿ

  积的乘方：(ab)ⁿ = aⁿbⁿ

• Power of a quotient: (a/b)ⁿ = aⁿ ÷ bⁿ

  商的乘方：(a/b)ⁿ = aⁿ ÷ bⁿ

Note: These rules require a > 0 so that they can be applied freely, especially with non-integer exponents.

注意：当指数为非整数时，需确保 a > 0 才能自由应用这些法则。

2. Fractional and Negative Exponents | 分数指数与负指数

Fractional exponents

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