知识点 8

Work with exponential expressions/equations and logarithms when presented.

Rewrite matching bases first, and read logarithms as exponent questions.

核心知识

For exponential equations, try rewriting both sides with the same base first. If a logarithm appears, treat it as another way to express an exponent.

深入理解

Rule: ACT exponential questions are usually about structure, not advanced log rules. If the bases can be rewritten to match, the exponents can be compared directly.

When a logarithm appears, read it as an exponent question. For example, log𝑏⁡𝑎 =𝑐 means 𝑏𝑐 =𝑎. Switching between those two forms is often all you need.

分步讲解

  1. Rewrite both sides with the same base when possible.
  2. Compare exponents once the bases match.
  3. If a logarithm appears, convert it to exponent form.

常见误解

  • Trying to compare exponents before the bases match.
  • Treating logarithms as unrelated notation instead of another way to write exponents.
  • Missing the simpler rewrite that makes the equation easy.
题目

示例解析

If 9𝑥 =27, what is the value of 𝑥?

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