Algebra

Closure Property of Addition

Sum (or difference) of 2 real numbers equals a real number

Additive Identity

a + 0 = a

Additive Inverse

a + (-a) = 0

Associative of Addition

(a + b) + c = a + (b + c)

Commutative of Addition

a + b = b + a

Definition of Subtraction

a - b = a + (-b)

Closure Property of Multiplication

Product (or quotient if denominator

0) of 2 reals equals a real number

Multiplicative Identity

a * 1 = a

Multiplicative Inverse

a * (1/a) = 1 (a

(Multiplication times 0)

a * 0 = 0

Associative of Multiplication

(a * b) * c = a * (b * c)

Commutative of Multiplication

a * b = b * a

Distributive Law

a(b + c) = ab + ac

Definition of Division

a / b = a(1/b)

x^a x^b = x^{(a + b)}

x^a y^a = (xy)^a

(x^a)^b = x^(ab)

x^(a/b) = b^th root of (x^a) = ( b^th

(x) )^a

x^(-a) = 1 / x^a

x^{(a - b)} = x^a / x^b

y = log_b(x) if and only if x=b^y

log_b(1) = 0

log_b(b) = 1

log_b(x*y) = log_b(x) + log_b(y)

log_b(x/y) = log_b(x) - log_b(y)

log_b(xⁿ) = n log_b(x)

log_b(x) = log_b(c) * log_c(x) = log_c(x) / log_c(b)

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