Regarding the use of logarithms

The question has arisen regarding the use of log base 10 (log or log₁₀) vs. log base e (ln). We call log base e the natural logarithm since it arises from the integral:

Of course, you can convert from ln to log using a constant multiplier.

On page 232 in Atkins the analysis of the reaction order and rate constant using the method of initial rates is performed using the log10 function. This could have been done using the ln function just as well.

The initial rate is given by

The analysis can proceed by taking the log

or the ln

as long as you are consistent.

Think of the log or the ln as a way to linearize data that has some kind of power law dependence. The only difference between these two functions is a scale factor (2.3025) in the slope. Obviously, if you multiply both sides of the equation by the same number the relative values of the constants remains the same on both sides.