Solution: It is almost enough to remember these logarithmic formulas of liberal arts mathematics in senior high school.

( 1)g(a)(MN)= log(a)(M)+log(a)(N)；

(2)log(a)(M/N)= log(a)(M)-log(a)(N)；

(3)log(a)(M^n)=nlog(a)(M)

(n∈R)

(4)log(a^n)(m)= 1/nlog(a)(m)(n∈r)

(5) the formula for changing the bottom: log (a) m = log (b) m/log (b) a/log (b) a.

(b>0 and b≠ 1)

(6)a^(log(b)n)=n^(log(b)a)

Prove:

Let a = n x then a (log (b) n) = (n x) log (b) n = n (x log (b) n) = n log (b) (n x) = n (log (b) a)

(7) Logarithmic identity: a log (a) n = n;

log(a)a^b=b

(8) This formula can be derived from the operational properties of logarithm of power.

1.log(a)m^( 1/n)=( 1/n)log(a)m

,

log(a)m^(- 1/n)=(- 1/n)log(a)m

2.log(a)M^(m/n)=(m/n)log(a)M

,

log(a)M^(-m/n)=(-m/n)log(a)M

3.log(a^n)M^n=log(a)M

,

log(a^n)M^m=(m/n)log(a)M