The base-changing formula is an important formula, which is used in many logarithmic calculations and is also the focus of high school mathematics.
Logs (a) and (b) represent logarithms based on b.
The so-called formula for changing the bottom is
log(a)(b)=log(n)(b)/log(n)(a)
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The derivation process of the bottom-changing formula;
Let a = n x and b = n y (n > 0, n is not 1).
rule
log(a)(b)=log(n^x)(n^y)
According to the basic formula of logarithm
Log (a) (m n) = nloga (m) Basic formula Log (a n) m =1/n× log (a) m.
Easy to obtain
log(n^x)(n^y)=y/x
X = log (n) (a) and y = log (n) (b) can be obtained from a = n x and b = n y.
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)