# How do you convert a logarithm to a different base?

##### 1 Answer

Oct 22, 2015

If you want to convert

#### Explanation:

Consider

From a definition of logarithm

(1)

Analogously, if

(2)

Finally, if

(3)

From (1) and (2) we derive

(4)

Using (3) and substituting

(5)

or, simplifying the left part,

(6)

From the last equation we see that

or, returning back to the meaning of