Two  properties of ‘log’ functions are proved below:
(1)
There is a standard change of base rule to obtain loga p in terms of logb p Let
loga p = α, logb p = β and logb a = γ This means aα = p, bβ = p and bγ = a Substituting the third equation in the first one, we have
(bγ)α = bγα = p
Using this in the second equation, we get
bβ = p = bγα
which implies
β = αγ or α = β
γ