ACTMediumFrequency: 1 - 2 questions
ACT Math Logarithm Laws & Change of Base
Logarithms are the inverse of exponentiation: log_b(x) = y means b^y = x. Key laws include log(ab) = log a + log b, log(a/b) = log a - log b, and log(a^k) = k log a.
Core Formula & Concept Cheat Sheet
1log_b(xy) = log_b(x) + log_b(y)
2log_b(x/y) = log_b(x) - log_b(y)
3log_b(x^k) = k · log_b(x)
4Change of base: log_b(a) = log(a) / log(b)
The 700+ Score Trap
Confusing log(x + y) with log(x) + log(y) (log does not distribute over addition!).
Test Your Mastery
Official Exam FormatLive Interactive Practice Drill
If log₃(x) + log₃(x - 6) = 3, what is the value of x?
Frequently Asked Questions
Can I solve ACT log problems on a TI-84?
Yes, use MATH -> logBASE( to evaluate logarithms of any base directly.