alvindavis99

CIP School in the Phils.

Algebra: Exponents

on August 23, 2012
English: Logarithms: red is ln(x), green is lo...

English: Logarithms: red is ln(x), green is log(x) base 10, purple is log(x) base 1.7 (Photo credit: Wikipedia)

Exponential Identities
 

Powers

x a x b = x (a + b)

x a y a = (xy) a

(x a) b = x (ab)

x (a/b) = bth root of (x a) = ( bth (root)(x) ) a

x (-a) = 1 / x a

x (a – b) = x a / x b

Logarithms

y = logb(x) if and only if x=b y

logb(1) = 0

logb(b) = 1

logb(x*y) = logb(x) + logb(y)

logb(x/y) = logb(x) – logb(y)

logb(x n) = n logb(x)

logb(x) = logb(c) * logc(x) = logc(x) / logc(b)

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