functions
Algebra
Logarithm Rules Cheat Sheet
Complete logarithm rules cheat sheet with product rule, quotient rule, power rule, change of base, and natural log properties. Free PDF download.
Basic Properties
| Name | Formula | Notes |
|---|---|---|
| Definition | b is base, x is argument | |
| Log of 1 | Any base raised to 0 is 1 | |
| Log of Base | Base raised to 1 is itself | |
| Log of Power | Inverse property | |
| Exponential of Log | Inverse property |
Logarithm Laws
| Name | Formula | Notes |
|---|---|---|
| Product Rule | Log of product = sum of logs | |
| Quotient Rule | Log of quotient = difference of logs | |
| Power Rule | Exponent moves to front | |
| Root Rule | nth root = divide by n |
Change of Base
| Name | Formula | Notes |
|---|---|---|
| Change of Base Formula | Convert to any base c | |
| Using Natural Log | Convert using ln | |
| Using Common Log | Convert using log₁₀ | |
| Reciprocal Rule | Flip base and argument |
Natural Logarithm (ln)
| Name | Formula | Notes |
|---|---|---|
| Definition | e ≈ 2.71828 | |
| ln(1) | ||
| ln(e) | ||
| ln(eˣ) | ||
| e^(ln x) |
Common Logarithm (log₁₀)
| Name | Formula | Notes |
|---|---|---|
| Definition | Base 10 logarithm | |
| log(1) | ||
| log(10) | ||
| log(10ⁿ) | ||
| log(100) |
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