SOLUTION: log(1.00417) how to see in the log table ?

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Question 739606: log(1.00417) how to see in the log table ?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
log(1.00417) how to see in the log table ?
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I don't have a log table. Well, there might be one somewhere here, but I don't use one.
I use a calculator.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%281.004%29=0.00173371 and log(1.005)=0.00216606}}}
To find an approximation of the log for numbers in between, we do highlight%28interpolation%29.
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
%28.00216606-0.00173371%29%2F%281.005-1.004%29=.00043235%2F0.001=0.43235
The equation of the line would be
log%28x%29-0.00173371=0.43235%2A%28x-1.004%29 (a point slope form of the equation)
or the equivalent log%28x%29=0.00173371%2B0.43235%2A%28x-1.004%29

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:
%28.00216606-0.00173371%29%2F%281.005-1.004%29=.00043235%2F0.001
The increase between log%281.004%29 and %7Blog%281.00417%29 will be proportional, so
%28log%281.00417%29-0.00173371%29%2F%281.00417-1.004%29=.00043235%2F0.001
%28log%281.00417%29-0.00173371%29%2F.00417=.00043235%2F0.001
%28log%281.00417%29-0.00173371%29=%28.00043235%2F0.001%29%2A0.00017
%28log%281.00417%29-0.00173371%29=0.00007350
log%281.00417%29=0.00173371%2B0.00007350=0.00180721