7.4 Expanding/Condensing Logs

log_b(mn) = log_b(m) + log_b(n) for any positive numbers m and n.

log_b(m/n) = log_b(m) - log_b(n) for any positive numbers m and n.

log_b(m^p) = p * log_b(m) for any positive number m and any real number p.

2^3 = 8.

5^2 = 25.

log_b(a) = log_k(a) / log_k(b) for any positive k.

log_10(1000) = 3 because 10^3 = 1000.

A logarithm is the exponent to which a base must be raised to produce a given number.

b^y = x.

0, because 10^0 = 1.