Logarithms — Formula Sheet

a^b = c ⇔ log_a c = b

log_x 1 = 0

log_x x = 1

log_10 1000 = 3

log_3(1/9) = -2

log_a a^x = x

log_a(m × n) = log_a m + log_a n

log_x(m × n × p) = log_x m + log_x n + log_x p

log_a(m)^n = n log_a m

log_a √[n]{m} = log_a m^(1/n) = (1/n) log_a m

log_a(m × n × p) = log_a m + log_a n + log_a p

log_10 2 + 1 = log_10 20

If log_a m = n, then a^n = m

If log_a x = b, then x = a^b

If a^b = c, then log_a c = b.

For any positive base x, x^0 = 1 gives log_x 1 = 0.

For any positive base x, x^1 = x gives log_x x = 1.

log_10 1000 = 3 because 1000 = 10^3.

log_a c = b means a^b = c.

These results come from x^0 = 1 and x^1 = x.

log_a(m/n) = log_a m - log_a n.