how to find the logarithm of Log10(4.7) using log table?

Question

hi guys how can i find the logarithm of Log10(4.7) manually by using a log-table, i have to learn it for my exams because we are not allowed to use calculators, but they allow us to use log-tables but in log-tables log starts from 10, 1 to 9 are not present there in log tables, but we have question like in which values are smaller then 10 like Log10(4.7), can you tell me how can i find log of those number's
Thank you

Answer 1

First by rule you will write log10(4.7) as



log10(4) + log10(7)



Now consider log10(4) as 4000 and find out the logarithm



In the same manner consider log10(7) as 7000 and find the logrithm



Add both the values and you'll get the answer



Hope this works .... u can verify your answer with calculator as it will show approx correct answer



Good Day!

Answer 2

You write



x= 10 ^y



log x = y



You have to

4.7= 10 ^y

y=log 4.7 to the base 10.



Use the calculus to check the result.



log 4.7 = 0.672



10^(0.672)=4.7

What noramlly you find that the value for 0.47

You have to multiply by 10

There the number of digits before the decimal sign is 1

You write 1-1=0

0.

Then using the log table find the value 0.4 and the column 7. This value you write

That is going to your log value.



To find the anti log

fnd the value. To that mulitply by (0+1)*10. This will give you the answer.

Answer 3

Log Base 10 Table

Answer 4

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Well, it all goes back to asking how they made these tables, back then in the 17th century onward, doesn't it? No choice but to calculate by hand. With a good knowledge of the log properties, one could interpolate to find better approximations. One could try to find a polynomial approximation for range of values; later, Taylor series surely helped; and other series approximation more accurate than Taylor could be found. But let's say you don't have a calculator, and you want to find log7, in base 10. So you're looking for x such that 10^x is close to 7. We do know how to calculate square roots, and we know powers of 10 add up upon multiplication (i.e. 10^m * 10^n = 10^(m+n) ). We can calculate (by hand): 10^(1/2) ~ 3.1623 10^(1/4) ~ 1.7783 10^(1/8) ~ 1.3335 10^(1/16) ~ 1.1548 10^(1/32) ~ 1.0746 ... and so on, taking the square root successively. Now: 10^(1/2 + 1/4) ~ 3.1623 * 1.7783 ~ 5.6235 (too small) 10^(1/2 + 1/4 + 1/8) ~ 3.1623 * 1.7783 * 1.3335 ~ 7.499 (too big) 10^(1/2 + 1/4 + 1/16) ~ 3.1623 * 1.7783 * 1.1548 ~ 6.494 (too small) 10^(1/2 + 1/4 + 1/16 + 1/32) ~ 3.1623 * 1.7783 * 1.1548 * 1.0746 ~ 6.9785 (too small, but closer)... So you see, we've found that 1/2 + 1/4 + 1/16 + 1/32 = 27/32 = 0.84375 is already quite close to log7 (base 10). A calculator gives us log7 ~ 0.845098... (base 10) which is 0.2 % close to our approximation. The above trick is just a hint of what can be done. Much more elaborate, precise and performant methods, coupled with courage, patience, and lots of dedication, made the log tables of those days. And once you have the tables, you can find the logs and anti-logs (with the help of the usual properties of log and exponential). Then came mechanical calculator, then electronic ones with tubes, then electronic ones with silicone chips... Oh, and there was an era with slide rulers... I remember portraits of mathematicians and physicists (Niels Bohr comes to mind), posing with their slide rulers in their hands, like a soldier posing with his gun... So it's quite refreshing seeing someone wondering how it's done without the ubiquitous calculators, math programs (like Mathematica, MatLab, etc) (I've got to admit... I didn't calculate those successive square roots by hand, I use the PC's calculator! But in principle, one could calculate those roots by hand... You forgive me? :P )

Answer 5

4.7 comprises of two parts,

integer=4 (in this case no of digits = 1)

fraction=7( can be any no of digits,but only 4 digits inclusive of integer are considered while looking log tables)

step1

subtract 1 from no of integer digits;1-1=0

step2

in the table you get numbers from 1.000 to 9.999 (some tables will have 1 to 9 in the first column and 0.1,0.2 ........0.9 in the next columns)

look for 4.700

you will get a value 6270.

step3

so the log = 0+.6270=0.6270.



if the number were to be 47 instead of 4.7,then log will be 1.6270

if the number were to be 476543 instead of 4.7,then log will be 5.6776 (for 476 that is,only for 3digits of the number for which you need the log)



practise any few numbers of 2,3,4,5,6 digit numbers to get the hang of the things.



trust, have not muddied your brain