The so-called bottoming formula is log(a)(b)=log(n)(b)/log(n)(a).

Deduction:

logarithmic

Log (a)(b)

Let a = n x and b = n y.

rule

log(a)(b)=log(n^x)(n^y)

according to

The basic formula of logarithm 4: log (a) (m n) = nlog (a) (m)

and

Basic formula 5: log (a n) (m) =1/n× log (a) (m)

get

log(n^x)(n^y)=y/x

pass by

a=n^x,b=n^y

get

y=log(n)(b)，x=log(n)(a)

Then there is: log (a) (b) = log (n x) (n y) = log (n) (b)/log (n) (a).

Proof: log(a)(b)=log(n)(b)/log(n)(a).