Logarithms

If a^b = c

If a^b = c, then b is called the logarithm of c at base a, written as log_a c = b. The condition a ≠ 1 must hold.

The statement a^b = c

The statement a^b = c is the exponential form, and log_a c = b is the logarithmic form. Both mean the same thing.

For any positive x

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

log_a(m × n) = log_a m

log_a(m × n) = log_a m + log_a n. The logarithm of a product is the sum of the logarithms of its factors.

log_a(m/n) = log_a m

log_a(m/n) = log_a m - log_a n. The logarithm of a fraction is the difference of the logarithms of numerator and denominator.