The Basic log equation

logx a = K where xK = a

So that:

log10 10,000 = K or 10K = 10,000 and K = 4

Basic Operations on logs of the same base

Addition

logx y + logx z = logx (y * z)

Subtraction

logx y - logx z = logx (y / z)

Multiplication

logx y * logx z = logx (y(logxz))

Division

logx y / logx z = logx (y(1/(logxz)))

Algebraic Operations for Base and Mantissa conversion

Most usefully: logx y / logx z = logz y

log10 16 / log10 2 = log2 16

Also:

logx y => logz y * K

Such that: logx y = logx y * logy z * logz y

Further: 1 = logy z * logz y