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)