SOLUTION: Another logarithm question: Calculate log 5601 using table. Not in table. Closest: 5599 = 363 5611 = 364 Difference of .001 Difference of 5601 - 5999 = 2 Dif

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Another logarithm question: Calculate log 5601 using table. Not in table. Closest: 5599 = 363 5611 = 364 Difference of .001 Difference of 5601 - 5999 = 2 Dif      Log On

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Question 1210626: Another logarithm question:
Calculate log 5601 using table.
Not in table.
Closest: 5599 = 363 5611 = 364 Difference of .001
Difference of 5601 - 5999 = 2
Difference of 5611 - 5601 = 10
Not sure how to proceed.


Found 4 solutions by josgarithmetic, greenestamps, timofer, ikleyn:
Answer by josgarithmetic(39823) About Me  (Show Source):
You can put this solution on YOUR website!
5601
5.601x10^3
The exponent 3 will be important. 
Find in the table for 5.60      0.748188

               diff.  0.01          d

Want for 5.601                      total diff. 0.000775

               diff.  0.009

Find in the table for 5.61      0.748963

Using these, find what is d.
d%2F0.01=0.000775%2F%280.01%2B0.009%29

d%2F0.01=0.000775%2F0.019

d=%280.01%2A0.000775%29%2F0.019
d=0.000408

You are looking first for
0.748188%2Bd
0.748188%2B0.000408
0.748996

Next, include the exponent from the original given number.
highlight%283.748996%29

quick-check using Windows Calculator:
log(5601)=3.748265

Answer by greenestamps(13355) About Me  (Show Source):
You can put this solution on YOUR website!


The calculations in the response from @jogsarithmetic make no sense.

The answer they come out with is 3.748996, and they show the correct answer (from a calculator) to be 3.748265. The answer they come out with should not be that far from the correct answer.

From a table, find

log(5.60) = 0.748188
log(5.61) = 0.748963

(Note that the answer from the other tutor for log(5601) is greater than log(5610), which makes no sense...)

You want to find log(5601) = log(5.601*10^3) = 3+log(5.601)

5.601 is one-tenth of the way from 5.60 to 5.61, so log(5.601) is (very nearly) one-tenth of the way from log(5.60) to log(5.61).

The difference between log(5.60) and log(5.61) is 0.748963-0.748188 = 0.000775

One-tenth of that difference is 0.0000775. So

log(5.601) = 0.748188+0.0000775 = 0.7482655

ANSWER: log(5601) = 3.7482655

Answer by timofer(159) About Me  (Show Source):
You can put this solution on YOUR website!
A better computation set up should be this. 
input         log
5.600         0.748188
5.601           ?
5.610         0.748963

letting d be how far from 0.748188 to the unknown part of the table, then
d%2F0.000775=0.001%2F0.01
d=0.0000775


log%285.601x10%5E3%29
3%2Blog%285.601%29
3%2B0.748188%2B0.000075
3.7482655
or better 3.74827

Answer by ikleyn(53875) About Me  (Show Source):
You can put this solution on YOUR website!
.

For a reader:


The difference / (the discrepancy) between the numbers 3.748996 and 3.748265
in the post by @josgarithmetic tells/indicates that the procedure used by @josgarithmetic in his post is ERRONEOUS.

In order to convince that a computational procedure is valid,
the discrepancy MUST be much lesser.

I do not try to explain it to @josgarithmetic or to convince him (since it is useless).

I only want to aware a reader: do not accept wrong recommendations.