Logarithm laws

Power law

logbpn = n * logbp

Proof:

logbp = a -> ba = p

Raise to k -> bk*a = pk

Apply logb -> k * a = logbpk

Replace a with logbp -> k * logbp = logbpk

Product law

logbm*n = logbm + logbn

Proof:

logbm = i -> bi = m & logbn = j -> bj = n

Multiply -> bi * bj = m * n

Simplify -> bi+j = m * n

Apply logb -> i + j = logbm*n

Replace i and j -> logbm + logbn = logbm*n

Quotient law

logbm/n = logbm - logbn

Proof:

logbm = i -> bi = m & logbn = j -> bj = n

Divide -> bi / bj = m / n

Simplify -> bi-j = m / n

Apply logb -> i - j = logbm/n

Replace i and j -> logbm - logbn = logbm/n