If a= 10m, then m is the common logarithm (decimal number) lga=m, and 10 is the base of the common logarithm. The properties and operation rules of logarithm are as follows:

(1) properties: ① loga (1) = 0;

②log 1；

③ There is no logarithm between negative number and zero.

(2) Algorithm: ① loga (Mn) = logam+Logan;

②loga(M/N)= logaM-logaN；

③ for the n power of m in logaM, there is = nlogam.

If a=em, then m is the natural logarithm of a, that is, lna=m, e = 2.7 18 18 … is the base of the natural logarithm.

(3) Bottom-changing formula

logaN=(logmN)/(logma)

(4) Derive the formula

log( 1/a)( 1/b)= loga(b)

loga(b)*logb(a)= 1

(5) Find the derivative

(logax)'= 1/xlna

Special, that is, a=e sometimes.

(lnx)'= 1/x