how to find logarithm of 0.04 its value is not in log table

[asal]

it is extremely difficult to find the log 0.04 from log table.calculator calculates its value to be -1.3979.but from log table i cant find its value.my log table begins from 10 th row and finishes off at 99th row.theres no log 4 or log 0.04 in the table.

 

[Deleted member 4993]

it is extremely difficult to find the log 0.04 from log table.calculator calculates its value to be -1.3979.but from log table i cant find its value.my log table begins from 10 th row and finishes off at 99th row.theres no log 4 or log 0.04 in the table.

What is the value of log(40) according to your table?

 

[Harry_the_cat]

\(\displaystyle log (0.04) = log (40* 10^-3)= log (40) + log (10^{-3}) = log (40) - 3 \)

Do you understand the steps above ?

Now use the log tables.

 

[asal]

its difficult to find logarithm with negative characteristic.

rules say one thing and calculator says different when finding log of negative characteristics.log 40 = 6021. i have four digit log table.my log table begins from tenth row and finishes off at 99th row. log 0.003634= -2.4396. characteristic of this is -3 but calculator shows -2.why? Rule say count the number of zeros after point and add one to it to find characteristic of a log.in our case -(2+1) = 3 is characteristic of log 0.003634. But calculator says its characteristic is -2.

 

[stapel]

rules say one thing and calculator says different when finding log of negative characteristics.

What "rules"? What do they "say"?

What, exactly, did you plug into the calculator? What did it "say"?

 

[Ishuda]

rules say one thing and calculator says different when finding log of negative characteristics.log 40 = 6021. i have four digit log table.my log table begins from tenth row and finishes off at 99th row. log 0.003634= -2.4396. characteristic of this is -3 but calculator shows -2.why? Rule say count the number of zeros after point and add one to it to find characteristic of a log.in our case -(2+1) = -3 is characteristic of log 0.003634. But calculator says its characteristic is -2.

Note than the 3 above should be -3. Also see
http://www.math-for-all-grades.com/CharacteristicandMantissa.html
for a possibly better explanation.

I believe you are misremembering the rule or applying it incorrectly. Lets take the example you have
log(0.003634) = -2.4396 = -2 - 0.4396
However, the mantissa must be positive so we have to write this as
log(0.003634) = -2.4396 = (-2-1) + (1-0.4396) = -3 + 0.5604
The mantissa is -3 (as you say). The calculator has just done that last addition for its final display.