How to calculate logarithm?

How to calculate logarithm?

The formula can be used flexibly as follows:
When a > 0 and a ≠ 1, M > 0, n > 0, then: (1) log (a) (MN) = log (a) (m) + log (a) (n); (2) log (a) (M / N) = log (a) (m) - log (a) (n); (2) log (a) (M / N) = log; (3) log (a) (m ^ n) = NLog (a) (m) (n ∈ R) (4) log (a ^ n) (m) = 1 / NLog (a) (m) (n ∈ R) (5) bottom changing formula: log (a) M = log (b) m / log (b) a (b > 0 and B ≠ 1) (6) a ^ (log (b) n) = n ^ (log (b) a) prove: let a = n ^ x, then a ^ (log (b) n = (n ^ x) ^ log (b) n = n ^ (x · log (b) n) = n ^ log (b) (n ^ x) = n ^ (log (b) a) (7) log identity: A ^ log (a) n = n; Log (a) a ^ B = B (8)