Loga(N)=x, then a x = n, and both sides take the logarithm with B as the base, logb (a x) = logb (n), xlogb(a)=logb(N), and x=logb(N)/logb(a), so Loga (n) =/kloc-.

The formula of changing base is a common logarithmic operation formula in high school mathematics, which can be used together with other logarithmic operation formulas. In the calculation, the calculation difficulty is often reduced, and the logarithmic operation in the middle and high schools can be solved faster.

Extended data:

Precautions:

Generally, the cardinality that is easy to calculate is selected according to the specific situation of logarithm.

Usually, when dealing with mathematical operations, the general base is converted into a natural logarithm with base E or a common logarithm with base 10, which is convenient for operation.

Using the logarithm-to-base formula, the logarithm of different bases can be transformed into the logarithm of the same base (first unify the base into an appropriate number as the base, and if the unified base is 10, it is a common logarithm).

Baidu encyclopedia-logarithmic exchange formula