Logarithms

A logarithm is the exponent to which a base must be raised to produce a given number. It is expressed as log_b(a) = c, meaning b^c = a.

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

4, because 3^4 = 81.

log_3(81) = 4.

3, because 3^3 = 27.

log_5(25) = 2.

-3, because 6^(-3) = 1/216.

The product rule states that log_b(m * n) = log_b(m) + log_b(n).

The quotient rule states that log_b(m / n) = log_b(m) - log_b(n).