Changing the Base

By definition, $x = b^{\log_b(x)}$ . Taking the log base $a$ of both sides gives

$$\log_a(x) = \log_b(x) \log_a(b)$$

which tells how to convert the base from $a$ to $b$ :

$$\log_b(x) = \frac{\log_a(x)}{\log_a(b)}$$

Thus, to change the base from $a$ to $b$ , divide by the log base $a$ of $b$ .