ACT Math Hard
⏱ 12 min 📊 Hard ⭐ Premium

Solving Logarithmic Equations

Method 1 — Convert to exponential form: log_b(x) = c quad Rightarrow quad x = b^c Method 2 — If both sides are logs with the same base: log_b(A) = log_b(B…

Theory

Solving Log Equations

Method 1 — Convert to exponential form: log_b(x) = c quad Rightarrow quad x = b^c Method 2 — If both sides are logs with the same base: log_b(A) = log_b(B) quad Rightarrow quad A = B Method 3 — Combine logs, then convert: Use log properties to combine into a single log, then convert. Always check: The argument of a log must be positive. Reject any solution that makes the argument ≤ 0.

Example: Solve log_2(x + 3) = 5

Summary

ACT Pro Tip

Most ACT log equations only require Method 1 (convert to exponential). If you see log_b(text{expression}) = text{number}, just rewrite as text{expression} = b^{text{number}} and solve the resulting algebra.

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