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).