Question 739606
I have not seen a log tables book in the last 40 years.
I found an easy to read one at http://www.sosmath.com/tables/logtable/logtable.html
That table said that:
{{{log(1.004)=0.00173371}}} and log(1.005)=0.00216606}}}
To find an approximation of the log for numbers in between, we do {{{highlight(interpolation)}}}.
Interpolation is the calculation of the approximate value of a function in between two known values, assuming that a straight line is a good approximation.
 
USING LINEAR FUNCTIONS DEFINITIONS:
The slope of the line would be
{{{(.00216606-0.00173371)/(1.005-1.004)=.00043235/0.001=0.43235}}}
The equation of the line would be
{{{log(x)-0.00173371=0.43235*(x-1.004)}}} (a point slope form of the equation)
or the equivalent {{{log(x)=0.00173371+0.43235*(x-1.004)}}}
{{{log(1.00417)=0.00173371+0.43235*(1.00417-1.004)=0.00173371+0.43235*0.00017=0.00180721}}}
Reading those logs in other tables may get a lot more complicated.
 
NOT MENTIONING LINEAR FUNCTIONS:
We are assuming that the increase in the log is proportional to the increase in the number.
We know the ratio for the increases in the points from the table:
{{{(.00216606-0.00173371)/(1.005-1.004)=.00043235/0.001}}}
The increase between {{{log(1.004)}}} and {{{{log(1.00417)}}} will be proportional, so
{{{(log(1.00417)-0.00173371)/(1.00417-1.004)=.00043235/0.001}}}
{{{(log(1.00417)-0.00173371)/.00417=.00043235/0.001}}}
{{{(log(1.00417)-0.00173371)=(.00043235/0.001)*0.00017}}}
{{{(log(1.00417)-0.00173371)=0.00007350}}}
{{{log(1.00417)=0.00173371+0.00007350=0.00180721}}}