exponants

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(x ⁿ) = n log_b(x)

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