ALLIED'S ELECTRONICS DATA HANDBOOK

How to Use Logarithms (cont.)

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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 (ab) = 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 four-place 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 122 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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