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whose mantissa is not exactly given in the table  Subtraction of logarithms  
1. 
Find the tabular difference between the next highest and next lowest man tissa. 
4.107 6.986 
= 
14.107  10 6.986 7.121  10 

2. 
Divide this by the differnece between the given mantissa and the next low est mantissa. 
11.672 5.785 5.887 
 10  10 

3. 
Add the resulting quotient to the significant figures expressed by the next lower mantissa. 
The relationships of logarithmic opera tions are expressed by the following formu las: 

4. 
Place the decimal as indicated by the given characteristic. 
log (a * b) log ( ^{a} / _{b} ) 
= = 
log a + log b log a  log b 

Example: Find the antilog of 1.7376  log (a^{b)}  =  b log a  
Next higher mantissa Next lower mantissa 
0.7380 0.7372 
=  
Tabular difference  0.0008  EXAMPLES  
Given mantissa Next lower mantissa 
0.7376 0.7372 
To Multiply
961 log of 1.24 
by = 
224 0.0934 

Tabular difference 0.0004 
0.0004 
log of 246 Total 
= 
2.3909 0.6325 

Quotient of  0.0008  =  0.5000  The antilog of 2.4843 = 305, which is as  
The resultant figure therefore is 0.5 larger than the significant figures expressed by the lesser mantissa 0.7372 or 546. The sequence 
accurate as can be determined with a four place table. The full answer to this prob lem is 305.04. 

of figures therefore is 546.5.  To Divide 961  by  224  
the antilog of 1.7376 = 54.65  log of 961  =  2.9827  
log of 224  =  2.3502  
Note: When interpolating as shown above, do not exceed four significant figures in your answer since interpolated results from a fourplace table are not accurate beyond this point. Logarithms are added or subtracted like arithmetical numbers, provided they are written with positive characteristics. If the characteristic in the total is greater than 9, and the notation 10, 20, 30, etc., appears after the mantissa, subtract a mul tiple of 10 from the positive part and add the same multiple of 10 to the negative part, so as to make the resultant character istic less than 10. 
Difference  0.6325  
The antilog of 0.6325 = 4.29 which is as accurate as can be determined with a four place table table. The product of 224 and 4.29 is 960.96 Powers: Find 12^{2} by logarithms: 

log of 12 
= 
1.0792 * 2 2.1584 

The antilog of 2.158 = 144.  
Roots Find  
log of 343 = 2.5353 / 3 The antilog of 0.8451 
= = 
0.8451 7.00 

EXAMPLES:

Logarithms of
Negative Numbers. Be cause the logarithms of negative numbers are imaginary in character, they cannot be used in computation as with positive num bers. However, since the numerical results of multiplying, dividing, etc., are not affected by the signs, you can determine the numerical results by logarithms and later affix the final + or  signs by inspection. 

Addition of logarithms  
2.764 4.304 7.068 
6.326  10 6.284 12.610  10 or 2.610 
6.328  10 7.764  10 9.104  10 23.196  30 or 3.196  10 

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