We can recognize logarithms as "fractions of exponential". Multiplying the same number with nominators and denominators, we can rewrite fractions with a different expression. Likewise, we rewrite logarithms with different expressions.
Formula. Change of Base (logarithm)
Using that formula, you can change the base of the logarithm and add (or subtract) logarithms with different bases, such as 
. So the change of base logarithm formula is the base of calculating logarithms.
Remark
Before proving the formula, we should understand the below formula.
Proof
This proof is a bit technical.
Dividing by 
, we get the formula.
Note
Physics often uses the base 10 and data are usually plotted in log scale charts with the base 10.
