Exponential Identities

Dave's Math Tables: Exponential Identities

(Math | Algebra | Exponents)

Powers

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

Logarithms
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)