You're forgetting that while the characteristic is negative, the basic numerical part of the decimal has a positive logarithm.prashant singh said:Log(0.0058) is ( -2.2365720064), its characteristic or integral part is (-2) but not (-3). As per rules of logarithm, Its characteristic or integral part must be (-3 ) because of two zeros plus 1 (as per rule) but its characteristic is (-2), similiarly log(0.0648) = -1.188424249941 but integral part must be (-2) but here it is (-1), I know why it is so but I only want to know why rule is getting wrong, if rule is wrong then why they made it. Please answer
prashant singh said:Wow great sir , u mean that the value which we get from log tables are not correct value unless we remove the dot sign between characteristic and mantisa with the plus sign, u mean that for example log(0.0000048) = 6`.68124 , this is a log table answer but it is not correct until we write it as -6 + o.68124 = -5.31875, original answer which matches with calculator. You mean that characteristic means from where we can start calculating logarithm and therefore it has bar symbol otherwise it may have only negative sign
SteamKing said:All I'm saying is that the log of a number less than 1 can be written in two different ways. If you use a calculator to calculate said log, you will get only one version of the log (-5.31875 to use the example above), not both.
The other version of the log, the so-called bar format (##\bar 6.68124##), can be used with log tables to calculate the logarithm in that manner, but you won't get it using a calculator to calculate the logarithm.
The bar-notation log value makes it easier on one who only has access to log tables. You still need to understand how to "decode" the bar-notation log value if you need to use it in other calculations, however.prashant singh said:Sir directly using the bar method in a question will be wrong or right , because bar method of finding the logarithm is not the correct value we have to simplify it and get the correct value
The value of log(0.0058) is -2.23657.
The integral part of log(0.0058) is -2.
The integral part of log(0.0058) is -2 because it represents the largest integer that is less than or equal to the given value. In this case, -2 is the largest integer that is less than or equal to -2.23657.
Logarithms can have negative values when the base is less than 1. In this case, the base is 10 and the given value is less than 1, resulting in a negative logarithm.
The value of log(0.0058) tells us that the original number is very small. In fact, it is less than 1, which is why the logarithm is negative. It also tells us that the original number is closer to 0 than it is to 1.