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urp:algebra [2021-11-08] nerf_herder |
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====Algebra & Pre-Calc==== | ====Algebra & Pre-Calc==== | ||
+ | Related pages: | ||
* [[Graphing|Graphing circles, ellipses, parabolas, hyperbolas]] | * [[Graphing|Graphing circles, ellipses, parabolas, hyperbolas]] | ||
* [[poly|Polynomials, quadratic formula and completing the square]] | * [[poly|Polynomials, quadratic formula and completing the square]] | ||
+ | * [[power|Powers, radicals (roots) & logs]] | ||
**quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | **quadratic formula**: x = (-b ±√(b²-4ac)) / 2a | ||
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S = n/2 (2a + (n − 1) d) | S = n/2 (2a + (n − 1) d) | ||
- | ==== Powers & Radicals ==== | + | ====Factorial==== |
- | + | ||
- | Combining powers | + | |
- | nᵃnᵇ = nᵃ⁺ᵇ | + | |
- | nᵃ/nᵇ = nᵃ⁻ᵇ | + | |
- | (nᵃ)ᵇ = nᵃᵇ | + | |
- | n⁻ᵃ = 1/nᵃ | + | |
- | + | ||
- | (Note: The square root sign, √, refers only to the //positive// root. Use ± to include both roots.) | + | |
- | + | ||
- | Factorial: | + | |
n! = n * (n-1)! | n! = n * (n-1)! | ||
0! = 1 | 0! = 1 | ||
7!/(7-3)! = 7!/4! = 7*6*5 * (4!/4!) = 7*6*5 | 7!/(7-3)! = 7!/4! = 7*6*5 * (4!/4!) = 7*6*5 | ||
- | |||
- | |||
- | ==== Logs ==== | ||
- | |||
- | Log is the inverse of a power | ||
- | x = bᵉ, e = logᵦ(x) (b = base, 10 by default) | ||
- | eg. 2³ = 8, log₂(8) = 3 | ||
- | log(1) = 0 (for any base), log(x) is undefined for x =< 0 | ||
- | logₐ(x) = logᵣ(x) / logᵣ(a) | ||
- | = log(x) / log(a) for r=10 | ||
- | = ln(x) / ln(a) for r=e (e = Euler's number, 2.718..) | ||
- | ln(e) = 1, log(10) = 1 | ||
- | ln(x) = logₑx. | ||
- | eᵏ = c, and k = ln(c) => e^ln(c) = c | ||
- | |||
- | a^logₐ(x) = x (power and log are inverses, cancel each other out) | ||
- | logₐ(aᵏ) = k (same reason) | ||
- | product rule: log(ab) = log(a) + log(b) | ||
- | quotient rule: log(a/b) = log(a) - log(b) | ||
- | power rule: log(aᵇ) = b*log(a) | ||
==== Functions ==== | ==== Functions ==== |