1, the logarithmic formula is a common formula in mathematics. If a x = n (a > 0, and a≠ 1), then X is called the logarithm of N with the base of A, and it is recorded as x=log(a)(N), where A should be written at the lower right of log. Where a is called the base of logarithm and n is called real number.

2. Usually, we call the logarithm with the base of 10 as the ordinary logarithm, and the logarithm with the base of e as the natural logarithm.

3. loga (1) = 0loga (a) =1,loga(MN)=logaM+logaN, loga (m/n) = logaM-logan, logaM (log (n) is equal to the n power of m in logam. (mn)=log(a)(m)+log(a)(n),log(a)(m÷n)=log(a)(m)-log(a)(n),log(a)(m^n)=nlog(a)(m),log(a^n)m= 1/nlog(a)(m)。

Derivation steps of the formula for changing the bottom

Let b = a m and a = c n, then b = (c n) m = c (Mn) ①.

For ①, the logarithm based on a is: log (a) (b) = m2.

For ①, the logarithm based on c is: log(c)(b)=mn③.

③/②、so:log(c)(b)/log(a)(b)= n = log(c)(a)∴log(a)(b)= log(c)(b)/log(c)(a)。