Module 2 · Algebra
Chapter 22: Logarithms
Algebra
4 topics
What this chapter covers
The 4 topics below make up Logarithms on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
The three laws
| Definition | log_b N = x ⇔ b^x = N (b > 0, b ≠ 1, N > 0) |
|---|---|
| Product law | log_b(MN) = log_b M + log_b N |
| Quotient law | log_b(M/N) = log_b M − log_b N |
| Power law | log_b(M^n) = n · log_b M |
| Log of base / of 1 | log_b b = 1, log_b 1 = 0 |
CAT power-tools
| Change of base | log_b a = (log a)/(log b) = (log_c a)/(log_c b) |
|---|---|
| Reciprocal rule | log_b a · log_a b = 1, i.e. log_b a = 1/log_a b |
| Base-power rule | log_(b^m)(a^n) = (n/m) · log_b a |
| Identity | b^(log_b N) = N and a^(log_b c) = c^(log_b a) |
| Digit count of N (base 10) | digits = ⌊log_10 N⌋ + 1 |
CAT reference
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